A top official at the World Health Organization (WHO) said Monday that a spike in the number of U.S. coronavirus cases is not solely the result of increased testing, a sign the virus is spreading widely in states across the country.

Nearly 60,000 new cases were identified in the United States over the weekend, the highest rate since the beginning of May. States such as Arizona, Texas, California and Florida have confirmed thousands of new cases each day for the past week.

Some have pointed to an increase in tests, which identify a larger number of asymptomatic and low-symptomatic COVID-19 cases, as the reason for the recent spikes.

But most of those states are also seeing an increase in the percentage of tests that come back positive, indicating the virus is spreading quickly. If the virus were stable, the percentage of positive tests would be declining.

"What is clear is that the increase [in cases] is not entirely explained through just increased testing. There is some evidence of increased hospitalizations. But this was always a possibility when restrictions were lifted," said Mike Ryan, who directs the WHO's emergency program overseeing the response to the pandemic.

More than 1 in 5 tests are coming back positive in Arizona, according to state data. The positivity rate is north of 10 percent and on the rise in Florida, South Carolina, Texas and Utah.

The number of coronavirus patients who have been admitted to the hospital is growing quickly in Arizona, Arkansas, North Carolina, Oklahoma, Oregon, South Carolina, Utah and Wyoming. In Texas, the number of people hospitalized has jumped 63 percent in the last two weeks.

The troubling rise in cases, positivity rates and hospitalizations may force some local governments to consider new lockdown measures to stem transmission. Ryan pointed to countries like South Korea, where local transmission has been snuffed out through robust local responses.

"There may be a need to put some restrictions in place in order to suppress infection," Ryan said. "We've seen countries do that at a micro level. Not at a state or a national level, but where needed."

Positivity and hospitalization rates have been falling in other states, especially those that were hit hardest by the virus early in the pandemic. The number of New Yorkers in the hospital has declined by half in the past two weeks, and just 1 percent of the tests conducted in New York are coming back positive.

Hospitalizations have fallen by more than half in Connecticut and Wisconsin, and by more than a third in Delaware, the District of Columbia, Illinois, Iowa, Maryland, Massachusetts, New Jersey and Pennsylvania.

Twenty-one states have the capacity to conduct more tests on a daily basis than their target goals, according to standards set by the Rockefeller Foundation's National Testing Action Plan.

The issue of testing was thrust back into the spotlight over the weekend after President Trump said he told staff to “slow the testing down, please.”

Trump on Monday refused to say whether he told staff to slow down COVID-19 testing to make it look like the U.S. had fewer cases, while White House officials denied he had ever given such an order.

Almost 2.3 million people in the United States have tested positive for the coronavirus, more than double the number of cases in any other nation and more than the next three most-infected nations — Brazil, Russia and India — combined. Just over 120,000 people in the United States have died, about a quarter of the global death toll.

There are hopeful signs that at least one drug, a steroid called dexamethasone, reduces mortality rates among those who have the most severe COVID-19 symptoms. A clinical trial in a hospital in the United Kingdom showed the drug helped reduce deaths in the worst cases by 20 percent to 33 percent.

WHO officials have lauded the finding. Director-General Tedros Adhanom Ghebreyesus said Monday that the WHO was confident that a global network of dexamethasone producers could ramp up production to meet what is likely to be substantial demand.

"Demand has already surged following the U.K. trials," Tedros said. "Fortunately, this is an inexpensive medicine."

But Tedros said the number of coronavirus cases remains dangerously high. More than 183,000 new cases were reported to WHO on Sunday, the highest single-day tally since the SARS-CoV-2 virus began circulating. Brazil alone accounted for more than 50,000 new confirmed cases over the preceding 24 hours, while the United States reported 36,000 new cases — its highest one-day tally since early May.

"It seems that almost every day we reach a new and grim record," Tedros said. "Some countries are continuing to see a rapid increase in cases and deaths."