Staff photo by C.B. Schmelter / Clinical Staff Leader Nurse Heather Atkinson adjusts the levels of medication for a patient inside the COVID-19 intensive care unit at Erlanger Medical Center on Feb. 22, 2021 in Chattanooga.

NASHVILLE, Tenn. (AP) — Tennessee hospitals warned Thursday that the intensive care units are full in nearly every hospital in the state's major metropolitan areas, pleading with Tennesseans to get vaccinated and wear masks while not going so far as to criticize Gov. Bill Lee's executive order allowing parents to opt their children out of mask mandates in K-12 schools.

Meanwhile, U.S. Education Secretary Miguel Cardona warned Tennessee in a letter sent Wednesday that the executive order might violate federal law.

(READ MORE: President Biden warns Gov. Lee, others who 'block and intimidate' locals schools into dropping mask mandates)

The Tennessee Hospital Association told residents in its statement the hospitals in metropolitan areas with full ICUs are the same ones that normally accept transfers from smaller hospitals of the sickest patients.

"This means that if you or a loved one need treatment for any type of serious healthcare problem like a severe injury, heart attack, or stroke, you may not be able to access the care you need, when you need it," the statement reads.

It cites Tennessee Department of Health data from May and July that found "at least 88% of these COVID hospitalizations and 94% of COVID deaths are among unvaccinated individuals."

Separately, a Vanderbilt University Medical Center and Vanderbilt School of Medicine report released Thursday found that hospitalizations have increased more than tenfold in a little more than a month, the fastest rate of increase seen during the pandemic.

"These trends suggest that if recent growth continues, Tennessee may soon eclipse high-water marks in ICU and ventilation use last seen in January," the report states.

It warns that while those people who have previously contracted COVID-19 have some immunity to the virus, research suggests they are twice as likely to become infected with the delta variant as vaccinated people. Also, while there are some breakthrough infections among the vaccinated, those infections rarely reach the severity of the infections among the unvaccinated.

In Shelby County, where a mask mandate for indoor public spaces begins Friday, hospital emergency department directors sent a letter to area mayors saying emergency rooms there are operating dangerously over capacity.

It is projected that hospitalized coronavirus patients will double by the end of the month and increase sixfold by the end of September in Shelby County, which is Tennessee's most populous and includes Memphis, the letter said.

"That increase would produce more admitted COVID patients than the city has hospital beds for on any normal day," the letter said. "These are greater numbers than we have yet faced in the pandemic and do not account for non-COVID patient emergencies such as stroke, heart attack and trauma."

Hospitals may have to begin choosing which patients receive care based on their probability of survival, the letter said.

Both the Vanderbilt report and the hospital group's statement emphasize that mask-wearing can help stop the spread of COVID-19. Lee's executive order Monday came after a few school districts issued mask requirements for their students. In Williamson County, where masking has been particularly divisive, 23% of elementary students have opted out of the mask requirement, according to an email from schools spokesperson Angie McKee.

The Republican governor's executive order does not apply to private schools that set their own mask mandates but would allow parents of private school students to opt out if the school was simply following a government-issued mask requirement.

Districts that have announced mask requirements for students and others entering the schools include Davidson County and Shelby County, the state's largest school district. Both districts said they would keep the mandates in place while reviewing Lee's order.

The Wednesday letter from Cardona supports the districts' rights to set their own policies.

"Tennessee's actions to block school districts from voluntarily adopting science-based strategies for preventing the spread of COVID-19 that are aligned with the guidance from the Centers for Disease Control and Prevention ... may infringe upon a school district's authority to adopt policies to protect students and educators as they develop their safe return to in-person instruction plans required by Federal law," it states.

The U.S. Education Department said on its website that policies that ban mask mandates could amount to discrimination if they lead to unsafe conditions that prevent students from attending school. The agency's Office for Civil Rights can issue a range of sanctions up to a total loss of federal education funding in cases of civil rights violations.

Lee's office did not respond to a request for comment on Cardona's letter.

As of Wednesday, 13,045 people had died in Tennessee from COVID-19.