School districts in Florida and Texas are bucking their Republican governors' bans on requiring masks for children and teachers as coronavirus cases soar in conservative areas with low vaccination rates.

The Broward County school board in Florida on Tuesday became the latest major district to flout an order by Republican Governor Ron DeSantis outlawing mask requirements in that state, prompting the administration of U.S. President Joe Biden, a Democrat, to say it was considering supporting the school districts financially if DeSantis retaliates against them by withholding funds from officials' salaries.

The Dallas Independent School District said late Monday that it would also require masks, despite an order banning such mandates from Republican Governor Greg Abbott.

The acts of rebellion by school officials come as these states -- along with Louisiana, Arkansas and others -- are flooded with new cases after people resisted vaccines and mask mandates. Teachers and administrators are seeking to protect students, many of whom are under 12 years old and cannot get vaccinated.

Fueled by the highly contagious Delta variant, U.S. cases and hospitalizations have soared to six-month highs with no flattening of the curve in sight.

Based on population, Florida, Louisiana and Arkansas are leading the nation with new cases and how many COVID patients fill their hospitals. Texas is not far behind.

In Arkansas, where only eight intensive care beds were available for COVID patients on Monday, Republican Governor Asa Hutchison said he regrets supporting a ban on mask mandates in his state.

In Florida, where nearly one out of every three hospital beds are occupied by a coronavirus patient, a surgeon in Orlando said hospitals in the area were "overflowing" with the unvaccinated.

"We need a field hospital. Please help us," Sam Atallah, a surgeon at AdventHealth wrote on Twitter on Monday. "We are in a state of emergency in Orlando."

In Dallas, where some staff had threatened to quit if masks were not mandated to protect children, teachers and others, school district officials said they did not believe the governor's order should be applied to them. Schools in Austin also plan to require masks.

"Governor Abbott's order does not limit the district's rights as an employer and educational institution to establish reasonable and necessary safety rules for its staff and student," the Dallas district said on its website.

Dallas County Judge Clay Jenkins, the county's top executive, said late on Monday that he asked a district court to block Governor Greg Abbott's July order that prevents local governments from implementing mask mandates.

"The enemy is not each other," Jenkins said in a statement. "The enemy is the virus, and we must all do all that we can to protect public health."

In San Antonio, officials also ordered masks to be worn in public schools, after a judge granted a temporary injunction to allow the mandate in a blow to Abbott.

In Florida, where lawsuits have also been filed challenging the anti-mask order, DeSantis has threatened to withhold salaries from school district officials who flout his ban.

The threat prompted a response from the administration of U.S. President Joe Biden, a Democrat, which is considering reimbursing school officials who lose their pay if DeSantis follows through on his threat.

"We're continuing to look into what our options are to help protect and help support these teachers and administrators who are taking steps to protect the people in their communities," White House Press Secretary Jen Psaki told reporters on Tuesday.

DeSantis stood by his statewide order banning mask mandates on Tuesday, saying it would allow parents to decide whether to mask their children for class.

"It's about parental choice, not government mandate, and I think ultimately, parents will be able to exercise the choices that they deem appropriate for their kids," DeSantis said at a briefing.

The Republican rising star is closely tied to former President Donald Trump, and DeSantis has become a national figure for opposing pandemic restrictions, even as Florida has become a hotbed of infections and hospitalizations have hit record levels.

DeSantis is widely seen as weighing a potential 2024 challenge for the presidency.