Florida's governor Ron DeSantis pleaded Monday for COVID-19 survivors to donate blood plasma to help save lives, as hospitals rapidly fill up and supplies of antiviral drugs run short.

The situation in the Sunshine State is dire, with more than 9,500 coronavirus patients hospitalised and just 18 percent of intensive care beds available.

Lines of people hoping to get a test can stretch for almost a mile and the results take seven to 10 days to come back, during which time contagious people can easily infect others.

On Monday, Florida reported 10,347 new cases and 90 deaths, bringing the total death toll to 5,072 in the new US epicenter of the outbreak.

The governor, who has come under fire for his handling of the public health response and his opposition to ordering people to wear face masks, was interrupted by protesters chanting "you're lying" as he made the appeal at the OneBlood donor center in Orlando.

Raising his voice over activists banging at the door, DeSantis called on Floridians to take tests for antibodies and to donate plasma if they test positive.

"There are people that had this with no symptoms a month or two ago that will have antibodies that can be used for this," the Republican governor said.

So-called "convalescent plasma" can be used to help infected people develop antibodies that stay in their own blood.

Plasma transfers have shown encouraging results in hospital patients.

"As quickly as the plasma comes in, it goes back out because that is the importance of the need," he said.