CHICAGO — The world has entered a “new and dangerous phase” of the coronavirus pandemic, a top official from the World Health Organization said Friday, a stark warning that came as the United States struggled to control spiraling outbreaks and as business leaders signaled growing unease with the country’s ability to effectively contend with the virus.

Coronavirus cases spiked sharply across the American South and West, particularly in states that loosened restrictions on businesses several weeks ago.

In Florida, Oklahoma, South Carolina and Arizona, daily counts of new coronavirus cases reached their highest levels of the pandemic this week. Texas, which has seen known cases double in the past month, became the sixth state to surpass 100,000 cases, according to a New York Times database of U.S. cases.

Around the country, there were indications that major companies and sports teams were changing their own plans as the new surges emerged.

Apple said it was temporarily closing 11 retail stores across four states amid an uptick in cases. AMC Entertainment reversed course on its mask policy Friday, saying it will now require patrons to wear face coverings when movie theaters reopen next month.

Two Major League Baseball clubs, the Philadelphia Phillies and the Toronto Blue Jays, and a professional hockey team, the Tampa Bay Lightning, abruptly shut down training facilities in Florida over concerns that the virus was threatening players’ safety.

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Across the globe, the outlook for containing the coronavirus worsened. A pandemic that had been defined early on by a series of shifting epicenters — including Wuhan, China; Iran; northern Italy; Spain; and New York — was now distinguished by a wide and expanding scope. Eighty-one nations have seen a growth in new cases over the past two weeks. Only 36 have seen declines.

“Many people are understandably fed up with being at home,” Dr. Tedros Adhanom Ghebreyesus, director general of the WHO, said in a news conference in which he described the new phase of the virus. “Countries are understandably eager to open up their societies and their economies. But the virus is still spreading fast. It is still deadly and most people are still susceptible.”

A sobering lesson in the virus’ tenacity came in China, where officials had recently proclaimed that they had vanquished the virus — only to see it surge back in Beijing, the capital. That metropolis, of 21 million people, is facing new restrictions on travel and renewed school closures. Seoul, South Korea, also reported a new surge in cases Friday.

For weeks, the U.S. has been slowly but determinedly returning to its pre-pandemic existence amid economic turmoil. Businesses reopened, summer camps started and retail workers returned to stores.

But efforts to boost the economy by bringing more people back to work may be happening too soon, experts said, warning that the economic outlook in the U.S. remains wildly uncertain.

Eric Rosengren, the president of the Federal Reserve Bank of Boston and an influential policymaker within the central bank system, cited rising caseloads in South Carolina and Florida as he cautioned of the economic impact of states reopening before the virus was under control. The tension between a tumbling economy and a global pandemic remained stark.

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In India, which placed all 1.3 billion of its citizens under a lockdown — then moved to reopen even with its strained public health system near the breaking point — officials reported a record number of new cases this week. And the virus is now spreading rapidly in Pakistan and Bangladesh.

Some countries where caseloads had appeared to taper — including Israel, Sweden and Costa Rica — are now watching them rise.

In Arizona and Texas, more people with the coronavirus are hospitalized now than at any previous point in the pandemic. In Utah, the percentage of positive tests compared with total tests reached the highest levels yet this month. In Nevada, the percentage of positive tests recently began increasing again after more than a month of sustained declines.

Alamo Drafthouse Cinema, a company with 41 theaters in 10 states, said Friday that it would require face masks in its theaters “except when eating or drinking,” saying the safety of patrons and workers could not be compromised. “This is not political,” the theater chain said in a tweet.

Regal Cinemas joined AMC and Alamo on Friday afternoon in stating that all movie theater employees and patrons would be required to wear masks. The chain, which had previously said it would require masks only in cities that mandated them, said that disposable masks would be made available to customers who needed them.

But a rival chain, Cinemark, began reopening some theaters in Texas on Friday without requiring face masks. “It’s a big country out there,” Mark Zoradi, Cinemark’s chief executive, told the entertainment news site Deadline on Wednesday. “There are places that may require it. California may be one. If it’s required in California, we’ll abide by it. There are other places like Texas where it’s not required. In those cases, we’ll highly recommend, but not require it.”

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All over, businesses were grappling with those sorts of decisions, as state rules have loosened and cases have risen. The possibility of repeated openings and closings was emerging.

Even as coronavirus cases increase in many states, there was reason for some optimism about the national picture overall. Coronavirus deaths in the U.S. have fallen to roughly 700 a day from a peak of more than 2,000 a day, and some of the country’s hardest-hit regions have showed sustained improvement. New case reports continue to plummet across most of the Northeast and much of the Midwest. The Chicago, Boston, Milwaukee, Detroit and New York areas all continue to improve.

But there were also worrisome signs in those same regions. Case numbers have started trending upward again in Kansas after weeks of falling. The La Crosse, Wisconsin, area is experiencing a period of explosive case growth. And new trouble spots have cropped up in parts of Missouri, Iowa and Pennsylvania.

As more Americans return to ordinary routines, clusters are emerging in places that had been largely closed. More than 230 cases were tied to a Pentecostal church in Oregon, and far smaller clusters were reported recently at churches in Alabama, Wisconsin and West Virginia. Outbreaks have also been reported recently at a Panda Express restaurant in California, an Advance Auto Parts store in Colorado, and among athletes at Kansas State University and the University of Texas.

South Carolina’s state epidemiologist pleaded with residents to wear masks and practice social distancing as that state identified more than 990 new cases of the virus Thursday. It was the sixth time in 10 days that the state broke its single-day case record.