he warning has echoed ominously for weeks from epidemiologists, small-town mayors and county health officials: Once states begin to reopen, a surge in coronavirus cases will follow.

That scenario is now playing out in states across the country, particularly in the Sun Belt and the West, as thousands of Americans have been sickened by the virus in new and alarming outbreaks.

Hospitals in Arizona have been urged to activate emergency plans to cope with a flood of coronavirus patients. On Saturday, Florida saw its largest single-day count of cases since the pandemic began. Oregon has failed to contain the spread of the virus in many places, leading the governor on Thursday to pause what had been a gradual reopening.

And in Texas, cases are rising swiftly around the largest cities, including Houston, San Antonio and Dallas.

“I’m very concerned about it,” said Mayor Eric Johnson of Dallas, noting that after months of warnings and isolation, many residents had stopped wearing masks and maintaining social distance out of sheer fatigue. “They’ve been asked for quite some time to not be around people they love, and that they want to spend time with. Wearing a mask is not pleasant. And I think people are tired.”

For close to a month, much of the United States has looked like a nation open or beginning to open, and increasingly unfettered by restrictions meant to slow the spread of the coronavirus. With many government limits removed and people left to make individual choices about precautions, Americans have gone back to salons and restaurants, crowded into public parks and, in dozens of cities, joined large public demonstrations protesting police misconduct.

Over all, daily coronavirus cases across the United States are essentially steady, stuck on a plateau. More than two million people have now contracted the virus in this country, according to a New York Times database, and every day, about 21,100 new known cases are reported, not much lower than the numbers from a month ago. About 800 people die from it each day. Those figures have both dropped significantly since peaking in April.

But as of Saturday, the daily number of new coronavirus cases was climbing in 22 states, shifting course from what had been downward trajectories in many of those places.

The spikes in cases bring leaders in these states to a new crossroads: Accept the continued rise in infections as an expected cost of reopening economies or consider slowing the lifting of restrictions aimed at stopping the spread or even imposing a new set of limits.

In Houston on Thursday, the county’s top elected official warned that the community was “on the precipice of a disaster” and urged residents to minimize contact with others. More than 300 new cases have been identified in that county on each recent weekday.

But at the city’s Galleria mall, there were few signs of concern: People stood in a tightly spaced line for pretzels at an Auntie Anne’s kiosk. At California Nails, two women sat maskless during pedicures. Signs urged social distancing, but in crowded walkways outside stores, shoppers brushed past one another, only inches apart.

Throughout most of Florida, the reopening of public life has allowed bars and movie theaters to operate at half capacity and gyms at full capacity. On June 5, the state loosened restrictions further, even as the caseload was beginning to go up.

In Salt Lake City, some people are now behaving as they did before the coronavirus pandemic, even amid a rise in cases, said Teresa Kehl, a Utah resident who runs summer soccer camps with her husband.

“We went to a restaurant the other night and none of the employees had masks on,” Ms. Kehl said. “It was kind of shocking.”

Dr. Angela Dunn, the Utah state epidemiologist, has traced the state’s resurgence in the coronavirus to the state’s reopenings, which began before Memorial Day.

“The timing directly correlates with our loosening up restrictions,” Dr. Dunn said. “That definitely has something to do with it.”

There is ample reason to tie the latest surge of infections to relatively early reopenings. Clusters of infections in food processing facilities, jails and nursing homes continue to create hot spots in some places, but they do not explain the broader pattern.

Most of the 10 hardest-hit states that have seen rising case levels started reopening on or before May 8. Louisiana, where cases have started rising again after extended declines, began reopening on May 15. Another hard-hit state with growing cases, California, has reopened in a more incremental way, with continuing restrictions in some regions.

Many states that were slowest to reopen have seen a different trajectory, at least so far. Most of the 10 states hit hard over all in the pandemic — but currently seeing decreasing daily cases of the virus — began reopening in mid-May or later. Only two of those states, Pennsylvania and Indiana, began reopening before May 15. Some of the others, New Jersey and Michigan, only began reopening in earnest in June. And two others, New York and Illinois, kept restrictions in their worst-hit areas while reopening less populous regions.

As testing capacity has increased, so has the number of cases being counted, and officials in places like Arizona and Florida say the increase in cases may be explained, at least partly, by the growing availability of tests.

Dr. Anthony S. Fauci, the country’s top infectious disease expert, said Friday in an interview with ABC News that it was important to look both at case numbers and the percentage of positive tests to understand whether upticks in cases reflected broader transmission in American cities.

“If you test more, you will likely pick up more infections,” Dr. Fauci said. He added, “Once you see that the percentage is higher, then you’ve really got to be careful, because then you really are seeing additional infections that you weren’t seeing before.”

But epidemiologists said that even taking into account a rise in testing, the increase in confirmed cases in Sun Belt states suggested increased transmissions. Other measures, such as the percentage of positive tests and hospitalizations, reflect that worsening outlook. In Florida more than 4.5 percent of those who tested between May 31 and June 6 had the virus, compared with about 2.3 percent of people who sought tests in mid-May. Earlier in the pandemic, the percent of people testing positive in Florida was higher, but that was during a period when testing was far more limited. Similar rates in Arizona and Texas have also risen in recent weeks.

In Arizona, more than 1,400 people who were believed to have the virus were hospitalized on Friday, up from 755 a month earlier and higher than at any other point in the pandemic. In Texas, the 2,166 coronavirus patients hospitalized on Friday were the most yet in that state.

For states with growing coronavirus outbreaks, some officials have arrived at the same conclusion: The rise in infections is unfortunate but inevitable.

“We are not going to be able to stop the spread,” said Dr. Cara Christ, the Arizona state health director. “And so we can’t stop living as well.”

But the outbreaks have also prompted frantic and repeated pleas to the public, asking that people wear masks and practice social distancing to limit transmission of the virus. On Thursday, Pat Gerard, the chairwoman of the Board of County Commissioners in Pinellas County, Fla., raised the specter of another clampdown on businesses to contain the latest outbreaks.

“I think it’s only a matter of time before the public sees those numbers and starts emailing us that we need to shut down again,” Ms. Gerard said during a board meeting.

For many business owners, the continued uncertainty about the path and the intensity of the pandemic has been vexing.

In Arizona, Gov. Doug Ducey, a Republican, moved energetically to reopen the state in May, and places like swimming pools, gyms and Little League fields have opened in recent weeks. Arizona officials reported more than 1,600 cases in a day for the first time on Friday.

Carla Logan, the owner of a bistro near downtown Phoenix, said that she was trying to save her business while making sense of Arizona’s rising number of cases. Theories by some scientists that the virus might diminish amid warmer weather were fading fast.

“We were hoping and praying the Arizona heat would kill the virus, but that didn’t happen,” she said. “A second shutdown for us would be catastrophic.”

In Florida, the number of new coronavirus cases has topped 1,000 for all but one of the past seven days. Most of the state began to reopen on May 4, though South Florida is still under tighter restrictions. Miami’s beaches only reopened on Wednesday.

Gov. Ron DeSantis, a Republican, has attributed the uptick to more widespread testing. Retail stores, including Publix supermarkets and Home Depot, now offer tests at a handful of locations, and state-run sites allow anybody to get tested, regardless of age or symptoms, without a doctor’s prescription. Even then, demand at some sites is low, and more than half of the available tests a day do not get used, the governor said.

In some ways, life in the state feels like it is getting back to normal. The Kennedy Space Center hosted the SpaceX launch. Jacksonville has been eager to host the Republican National Convention. Orlando has allowed the filming of professional wrestling and expects to soon welcome the National Basketball Association and Major League Soccer.

Despite the uptick in cases in some states, there are also states that have been reopened for weeks where the number of new known virus cases has slowed. Pennsylvania, Indiana and Colorado — which all began reopening in late April or early May — have seen hopeful signs.

It is possible that the full effect of reopening may be hidden from view. Certain states and counties are testing less than others. And reopening has looked different in different places, partly depending on varying habits of residents.

In places where masks are standard and people are adhering to social distancing — both recommended by public health experts — transmission may be slower.

In Douglas County, Kan., home to 122,000 people, only 82 cases of the coronavirus have been identified, an exceedingly low number for a place of its size.

The county, which includes the college town of Lawrence, kept in place restrictions on businesses even after statewide mandates were dropped. Residents have continued to wear masks and stay far apart, said Dan Partridge, the director of the local public health agency.

“The worry I have is that fatigue will set in and compliance will slip,” Mr. Partridge said.

Epidemiologists point to another factor that could result in even more coronavirus outbreaks in the coming days: the widespread demonstrations across the country, where protesters are packed shoulder-to-shoulder, often without masks.

Minneapolis, where protests erupted after the death of George Floyd, is being watched especially closely, though health officials say that it is too soon to know what effect the demonstrations had on the virus.

A small number of Minnesota National Guard members mobilized for the protests have tested positive, and new testing sites have been established for demonstrators.

At least 30 cases nationally have been linked to protests, including 10 National Guard members and one police officer in Nebraska who have been infected. Contract tracers in Chicago and elsewhere have begun asking people who are positive for the coronavirus whether they have attended protests.