A new week begins with a grim outlook: More than 100,000 new cases were identified over the weekend.

More than 100,000 new coronavirus cases were identified. Seven states set daily case records. Florida added more infections in a day than any state had previously.

And that was just over the weekend.

The U.S. outbreak — once centered in the densely packed northeastern hubs of New York and New Jersey — is now growing across 39 states, from the worsening hot spots in the South and West to those emerging in the Midwest. Restrictions on business operations, mass gatherings and mask-wearing have become debate fodder in an increasingly polarized election year.

As a new week begins, the country’s outlook is exceptionally grim. Case numbers are rising in all but a handful of states. Hospitals are running out of beds. And some of the country’s biggest urban centers — Atlanta, Dallas, Los Angeles, Miami, Phoenix, Jacksonville, Fla. — have seen out-of-control growth with few concrete signs of progress.

“Put politics aside and wear a mask,” Mayor Lenny Curry of Jacksonville, a Republican, said on Twitter.

As new cases continue to mount in the Southeast and West, troublesome signs are emerging elsewhere in the country. The county that includes Oklahoma City has been averaging twice as many cases as it was just two weeks ago. Case numbers have started increasing again around Minneapolis after weeks of progress. And Wisconsin and Ohio are averaging more new infections than at any previous point in the pandemic.

In Miami-Dade County, Fla., six hospitals have reached capacity as virus cases spike. The increase in cases caused the mayor there to roll back reopening plans by imposing a curfew and closing restaurants for indoor dining.

The move to treat Dr. Fauci as if he were a warring political rival comes as he has grown increasingly vocal in his concerns about the national surge in coronavirus cases. He has also noted his lack of access to Mr. Trump.

Aides to Mr. Trump released to The Washington Post and other news outlets a list of remarks Dr. Fauci made about the virus when it was in its early stages. It featured several comments White House aides had privately complained about for months.

An official told The Post that several other officials were concerned about how often Dr. Fauci had been wrong.

For example, White House officials pointed to a statement he made in a Feb. 29 interview that “at this moment, there is no need to change anything that you’re doing on a day-by-day basis.”

But they omitted a warning Dr. Fauci delivered right after.

“Right now the risk is still low, but this could change,” he said in the interview, conducted by NBC News. “When you start to see community spread, this could change and force you to become much more attentive to doing things that would protect you from spread.”

Dr. Fauci works for the Trump administration, but the list of his statements was laid out in the style of a campaign’s opposition research document.

A poll conducted for The New York Times by Siena College last month showed that 67 percent of Americans trusted Dr. Fauci when it came to the virus; only 26 percent trusted the president.

In an interview with FiveThirtyEight.com last week, Dr. Fauci said that a few states had the virus under control but that “as a country, when you compare us to other countries, I don’t think you can say we’re doing great. I mean, we’re just not.”

Last week, Mr. Trump told Fox News that Dr. Fauci had been wrong about many aspects of the pandemic. Dr. Fauci “is a nice man, but he’s made a lot of mistakes,” the president said.

Hong Kong, a city that weeks ago seemed like one of the most successful places in controlling the virus, announced Monday evening that it would close gyms and cinemas and ban public gatherings of more than four people in response to a new wave of locally transmitted infections.

Carrie Lam, the territory’s chief executive, announced a series of measures to take effect on Wednesday. Also included were a prohibition on all dining inside restaurants every evening from 6 p.m., and a requirement that everyone taking public transport wear a mask.

Health officials said that the territory’s new spate of cases, including another 52 announced on Monday, was mainly connected to taxi drivers, restaurants and nursing homes.

The prohibition on public gatherings of four or more people could make it even harder for the pro-democracy opposition to organize any protests against a stringent national security law imposed on June 30 by Beijing. The ban could also interfere with an election campaign now underway to choose a new legislature on Sept. 6.

Hong Kong, a semi-autonomous Chinese territory, has a robust contact-tracing system that helped the authorities contain an initial outbreak last winter. The city won praise from international health experts in the pandemic’s early days. In response to a second wave of infections imported in March from Europe and the United States, Hong Kong closed its borders to non-residents and mandated quarantine for returning residents.

The 52 new cases on Monday continued a week-long spike, labeled a third wave by health officials, after months in which few or no new daily infections were detected. The authorities said they were unable to trace the infection pattern in 20 of the new cases disclosed on Monday. That raises the prospect that the virus is circulating silently in the community, after months in which local transmission appeared to have been at a standstill.

Gabriel Leung, the dean of Hong Kong University’s faculty of medicine, said in a radio program on Sunday that the virus was now spreading at a faster pace within the region because of a mutation in its DNA. The reproductive number of the virus is currently close to four, he said, suggesting that each person who is infected on average passes the virus on to four others.

Reducing health risks by shifting life outdoors.

In Monday’s edition of The Morning newsletter, David Leonhardt discussed some of the creative ideas that companies, government agencies and other organizations have had to move activities outside, where the coronavirus spreads less easily:

Rice University, in Houston, is building nine big new classrooms this summer, all of them outdoors.

Five are open-sided circus tents that the university is buying, and another four are semi-permanent structures that workers are building in an open field near dorms, Kevin Kirby, Rice’s vice president for administration, told me. Students and professors will decorate the spaces with murals and video projections.

In the fall, the structures will host classes and student activities, while reducing health risks — since the coronavirus spreads less easily outdoors. Kirby describes the construction project as “a statement to the community.” The statement: “We’re creative. We’re resilient. And what we do matters.”

Across the country, many indoor activities are going to be problematic for the foreseeable future: school, religious services, work meetings, cultural events, restaurant meals, haircuts and more. Mask-wearing reduces the risks, but being outdoors can reduce it even more.

Do you know of other companies or communities taking smart steps to move activities outdoors? Tell us about it.

A virus outbreak on United States military bases in Okinawa, Japan, has alarmed the island’s local population, which has at times been at odds with the Americans stationed there, and has otherwise been successful in limiting Covid-19.

The U.S. Marine Corps, which has about 20,000 troops stationed on the island, reported 94 confirmed cases to the prefectural government and said it had instituted strict measures in all 33 installations in the region. The Japanese military, by contrast, has reported just 14 cases among its defense forces, all of whom are thought to have contracted the virus in their communities rather than while deployed.

Denny Tamaki, the governor of Okinawa, said he was shocked by the number of infections and said it was “extremely regrettable” that so many cases had emerged among American troops and affiliated personnel in less than a week. Excluding the American cases, Okinawa has recorded just 148 infections since February.

Mr. Tamaki added that he had “strong doubts” about the prevention measures reported by the United States.

The cases in Okinawa are a new strain on relations between the military and the local government, where the presence of American bases, dating to the end of World War II, has been a continuing source of friction. Citizens have long complained of noise, crime and aircraft accidents, and have repeatedly questioned why nearly half of the 55,000 American troops in Japan — which include personnel from all of the military branches — are stationed on Okinawa.

In other developments around the world:

• Australian citizens and residents returning from overseas to New South Wales, which includes the city of Sydney, will be charged for their mandatory 14-day hotel quarantine starting Saturday, the state premier said. Mandatory hotel quarantines at a similar cost are already in effect in Queensland and the Northern Territory, and other parts of the country are likely to begin charging travelers as well amid a new outbreak in Melbourne, Australia’s second-biggest city. The border has been closed to nonresidents since March.

• The leader of Spain’s northeastern region of Catalonia, Quim Torra, said on Monday that his government would proceed with a regional lockdown, a day after a judge ruled that such a measure was only valid if approved by the country’s central government.

• President Cyril Ramaphosa of South Africa reinstated a ban on the sale and distribution of alcohol in an effort to alleviate pressure on the health care system. The government also reintroduced an overnight curfew. South Africa has seen a surge in cases as the country enters its coldest month, with more than 264,000 known cases, and nearly 4,000 deaths, according to a New York Times database.

• Xu Zhangrun, a law professor in Beijing who had criticized the Chinese government’s handling of the coronavirus outbreak, was released from detention on Sunday, a week after the police took him away.

• In Hong Kong, a Department of Health spokeswoman said the Chinese territory’s latest outbreak was worse than a peak in March because of a growing number of cases with unknown origins and clusters linked to housing estates, homes for older people and restaurants. Hong Kong recorded 38 new infections and 20 preliminary positive cases on Sunday. The authorities on Monday canceled the city’s annual book fair, which was scheduled for Wednesday and typically draws large crowds.

After Trump first wore a mask in public, administration officials urge the public to do so, too.

Facing questions about the gravity of the nation’s coronavirus crisis, Trump administration health officials on Sunday took a somber tone and stressed the importance of wearing masks, something their boss did publicly for the first time only the day before.

On ABC’s “This Week,” Adm. Brett Giroir, an official with Health and Human Services, acknowledged that with “more cases, more hospitalizations,” the expectation was for “deaths to go up” over the next several weeks. “It’s really essential to wear masks,” he said, adding: “We have to have like 90 percent of people wearing the masks in public in the hot spot areas. If we don’t have that we will not get control of the virus.”

The host, George Stephanopoulos, asked about suggestions by President Trump — who after months of refusing, donned a mask on Saturday during a visit to Walter Reed National Military Medical Center — that there could be some harm in wearing face coverings.

“There’s no downside to wearing a mask,” Admiral Giroir said. “I’m a pediatric I.C.U. physician. I wore a mask 10 hours a day for many, many years.”

Asked if states with stark increases in cases, like Florida, South Carolina, Arizona, Texas and Georgia, should consider more stringent measures, Admiral Giroir said that closing bars and limiting the number of patrons allowed in restaurants are “two measures that really do need to be done.”

The admiral, who has been in charge of testing, also told NBC’s “Meet the Press” that rates of people testing positive were “leveling off.” However, the Covid Tracking Project at The Atlantic shows positivity rates leveling only in the Northeast, with rates rising in the South, West and Midwest.

Surgeon General Jerome Adams said people needed to “understand the importance of wearing face coverings and good hand hygiene and staying home when they can.”

Dr. Adams wore a mask during his entire interview on the CBS program “Face the Nation” even though he was being interviewed remotely from Indiana. He said measures like wearing face coverings were “critically important.”

With the virus surging in many parts of the country, a number of governors, mayors and county officials who had been hesitant about requiring face coverings have now issued mandates.

In all, 25 states and the District of Columbia now have face-covering orders in effect, and two more will join them on Monday, according to a tally by The New York Times. Twelve of the orders have come into force in July.

In general, the orders require most people to cover their faces when in public places and unable to maintain social distance. But the scope of the mandate varies from state to state.

A health worker in Italy raised concerns about the coronavirus. Then he lost his job.

In February, Hamala Diop, a 25-year-old medical assistant, said the directors of the nursing home where he worked in Milan kept him from wearing a mask, fearing it would scare patients and their families. In March, he became infected with coronavirus and spoke out about the virus spreading through the home. In May, he was fired amid claims that he had “damaged the company’s image.”

Mr. Diop challenged the decision in a lawsuit that will be heard in court on Monday. The proceedings raise the issue of whether whistle-blowers have paid a price in voicing concerns about dangerous conditions at medical facilities.

After successfully lowering the curve of new cases after a devastating initial outbreak, Italy is now bracing for a potential second wave.

The country, with the oldest population in Europe, was affected especially deeply by the virus, and nearly half the infections reported in April happened in nursing homes, according to the Italian National Institute of Health. The breadth of the outbreak put the management of nursing homes under judicial and media scrutiny.

In a statement, the lawyers for the nursing home, the Palazzolo Institute of the Don Gnocchi Foundation, said the home had followed the instructions of the Italian National Institute of Health on the use of masks, and that communications about the infections among workers took place according to privacy laws.

“Nobody protected us from catching the virus,” Mr. Diop said, “and nobody protected us from getting fired.”

That exodus came just as the once-a-decade census was getting underway. Now, census officials say wealthier neighborhoods in Manhattan are unexpectedly proving some of the hardest to reach.

Some of these census tracts include the city’s most exclusive stretches of real estate, like the Fifth Avenue corridor between 70th and 35th Streets, which the planning department said was “home to some of the lowest levels of self-response in the city.”

Only 46 percent of Upper East Side households have filled out their census forms, according to a June 25 report circulated by the Department of City Planning’s chief demographer, Joseph J. Salvo — well below the neighborhood’s final response rate in 2010, and short of the current citywide rate of almost 53 percent.

Only about 38 percent of households in Midtown Manhattan have filled out their census forms — the second-worst response rate in all of New York City, after North Corona, Queens, which is at about 37 percent.

The rate is only slightly better in the area encompassing SoHo, Tribeca and Little Italy, which is home to wealthy residents as well as many college students; those tracts have response rates of about 46 percent.

The undercount could have a dramatic effect, according to the department’s report. “Missing just one person in the city could reduce education funding by $2,295, and job training by $281,” it said.

Officials hope that many of the coronavirus evacuees will return by the end of October, the new extended deadline for final responses to the census.

After closing in March because of the pandemic, two of Walt Disney World’s major parks, the Magic Kingdom and the Animal Kingdom, welcomed back a limited number of temperature-checked visitors over the weekend, with some attractions and character interactions unavailable as safety precautions.

Epcot and Disney’s Hollywood Studios were set to reopen on Wednesday.

“I’m so overwhelmed with emotion,” said a weeping Sonya Little, who flew to Orlando, Fla., from Birmingham, Ala., with two friends. “The last few months have been so hard. We have just felt so defeated. Being here gives me the strength to go on.”

The reopening comes as the coronavirus continued its rampage through Florida, with officials reporting more than 15,000 new infections on Sunday, a daily record for any state.

To ward off germs, Disney now leaves rows of seats empty on rides, which employees constantly disinfect. Face masks are mandatory, and, for some visitors, the coverings quickly grew wet with sweat.

“It would be a lot more fun without having to wear one,” Ivan Chanchavac, 14, said as he hopped off the Jungle Cruise.

A choke point for the U.S. coronavirus response: fax machines.

Sometimes, they arrive instantly in a doctor’s email inbox. Other times, they are delivered physically, in envelopes. And still, a number of them are spit out by fax machines.

Across the United States, public health officials and private laboratories have dramatically expanded the number of coronavirus tests performed daily. But the system for recording those results, officials say, has remained fractured and disjointed.

The machine at the Harris County Public Health department recently became overwhelmed when one laboratory sent a large batch of test results, spraying hundreds of pages all over the floor.

“Picture the image of hundreds of faxes coming through, and the machine just shooting out paper,” said Dr. Umair Shah, executive director of the department. The county has so far recorded more than 40,000 coronavirus cases.

Some doctors fax coronavirus tests to Dr. Shah’s personal number, too. Those papers are put in an envelope marked “confidential” and walked to the epidemiology department.

“From an operational standpoint, it makes things incredibly difficult,” Dr. Shah said. “The data is moving slower than the disease.”

The torrent of paper data led at least one health department to request additional forces. Washington State recently brought in 25 members of the National Guard to assist with manual data entry for results not reported electronically.

Reporting was contributed by Brooks Barnes, Pam Belluck, Emma Bubola, Keith Bradsher, Chris Buckley, Sheri Fink, Kimiko de Freytas-Tamura, Hailey Fuchs, Maggie Haberman, Hikari Hida, Makiko Inoue, Sarah Kliff, Tiffany May, Raphael Minder, Zach Montague, Kate Phillips, Motoko Rich, Rick Rojas, Dana Rubinstein, Margot Sanger-Katz, Mitch Smith and Eileen Sullivan.