Three states just broke records for new COVID-19 cases. But their governors vow to stay open.

Corky Siemaszko

Florida, Texas and Arizona set records for new COVID-19 cases, and more than a dozen other states are also reporting big jumps in the number of cases as much of the country reopens after months of quarantine.

Are the governors in the worst-hit states considering another shutdown? Not a chance, if you ask them.

“No, we’re not shutting down, you know, we’re going to go forward,” Florida Gov. Ron DeSantis said Tuesday. “You have to have society function.”

Never mind that the Sunshine State recorded 2,610 new cases Wednesday -- just below Tuesday's record of 2,783 -- and the death toll rose from 2,993 to 3,018.

Texas Gov. Greg Abbott said he, too, is not considering closing the state down.

“We are better prepared to deal with COVID-19 today than we were back in March and April,” he said.

So what about the nearly 85 percent increase in COVID-19 hospitalizations since Memorial Day, from 1,511 to 2,793?

“There are some explanations for why these numbers are so high,” Abbott said. “It could be Memorial Day celebrations. It could be bar settings.”

Later Tuesday, the Texas state health department reported 2,622 new cases, plus an additional 1,476 state prison inmates who had previously been diagnosed with the virus.

In Arizona, state health officials reported 1,827 new coronavirus cases and 20 additional deaths Wednesday. On Tuesday, 2,392 cases were reported.

With the numbers continuing to rise, 700 medical providers sent a signed letter to Gov. Doug Ducey on Monday, warning that the hospitals in the state were in danger of being overwhelmed and pleading with him to mandate the use of masks in public.

“Since the reopening of Arizona’s economy, our health risk has drastically increased,” their letter states. “The sad fact is that nothing has changed regarding COVID-19 since the Stay at Home Executive Order was put into effect on March 31. Since the Executive Order was lifted, many Arizonans believe something has changed, and it is somehow now safe to resume normal life. Sadly, this is far from the truth.”

Ducey has recommended that people wear masks in public to combat the spread of the coronavirus, but he has refused to impose a statewide mandate, leaving it to local mayors to decide whether to penalize people for not wearing them.

"I am in favor of masks," Ducey said during a press conference Wednesday. "I want to see all Arizonans wearing face coverings."

The Ducey administration has also suggested that increased testing may be behind the surge in new cases.

Marcy Flanagan, director of Arizona's Maricopa County Department of Public Health, insisted last week that “these increases are not due just to an increase in testing that is occurring.”

State Rep. Kelli Butler, the Democrats' ranking member on Arizona's House Health Committee, echoed Flanagan.

“While the COVID-19 crisis in Arizona is becoming one of the worst in the world, we’ve seen Gov. Ducey and his staff spending more time trying to deflect criticism and spar with health experts and reporters than work on actual solutions to mitigate the spread of disease,” Butler said. “With President Trump scheduled to visit Arizona next week, I do wonder if the governor is doing more right now to please Trump than keep Arizonans safe.”

NBC News has reached out to Ducey’s spokesman Patrick Ptak for comment, but has not received a response.

DeSantis, Abbott and Ducey are all Republicans and strong supporters of President Donald Trump, who has taken heat for his administration’s slow response to the pandemic.

Trump did not declare a national emergency until March 13. And so far, about 118,000 people in the United States have been killed by the virus.

The president has also been pushing for a quick reopening of the economy. Over the objections of local health officials, Trump intends to hold a rally Saturday in Tulsa, Oklahoma. It will be his first since the country was shuttered to combat the coronavirus.

Vice President Mike Pence has praised Oklahoma for being “at the forefront of our efforts to slow the spread.” He also made the false claim that Oklahoma under the leadership of Gov. Kevin Stitt, a Republican and a Trump supporter, has “flattened the curve.”

But Oklahoma health officials reported a state-high daily total of 259 cases Tuesday and 76 of those were in Tulsa, the Tulsa World reported.

"Any rational person looking at any large grouping of people would have concerns about this weekend," Tulsa Mayor G.T. Bynum, a Republican, said.

Louisiana is also seeing a recent spike in new COVID-19 cases. Other states where COVID-19 cases continue to be on the rise are Alabama, Alaska, Arkansas, California, Georgia, Hawaii, Idaho, Montana, Nevada, North Carolina, Oregon, South Carolina, Utah, Vermont and Wyoming, along with the commonwealth of Puerto Rico.