Mr Trump, who is trailing Democrat Joe Biden in polling, has even threatened to cut federal funding for those schools that refuse to open their doors.
"The president has said unmistakably that he wants schools to open," White House spokeswoman Kayleigh McEnany said on Thursday. "And when he says open, he means open and full, kids being able to attend each and every day.
"The science should not stand in the way of this," Ms McEnany added. "The science is on our side here."
A Yahoo News/YouGov poll published Thursday found that 63 per cent of Americans said Mr Trump should not be pressuring schools to reopen, while 25 per cent agreed with his push.
Ninety-five per cent of the Democrats and 58 per cent of the Republicans surveyed agreed that reopening schools should take a back seat to public health.
Mr Trump and Mr DeSantis have only so much leverage, however, in a fight that has them butting heads with teachers' unions, medical experts and many wary parents.
State and local officials have the final say when it comes to their school districts.
The Houston school district, which has more than 200,000 students, plans to begin the school year virtually on 8 September and start in-person classes on 19 October "subject to change based on COVID-19 conditions."
Once in-person classes resume, "parents will have the option to opt out of face-to-face instruction entirely," it said.
The Los Angeles school district, with 700,000 students, said classes will be online-only until further notice.
In New York City, which has the nation's largest public school system with 1.1 million students, Mayor Bill de Blasio said classroom attendance would be limited to one to three days a week.
Other major cities, including Chicago and Washington, have kept parents on tenterhooks and not yet announced plans for the fall semester.
New record again
Florida reported a record 156 COVID-19 deaths on Thursday and nearly 14,000 new infections.
The total number of virus cases in the "Sunshine State" has now surpassed 315,000 and there have been 4,782 deaths, according to Florida Department of Health figures.
The reporting of 156 virus deaths in the state in a 24-hour period surpasses the previous high of 132 deaths announced just two days earlier.
Florida is now reporting more COVID-19 cases daily than any other state in the country. California and Texas are next with about 10,000 new cases a day.
The number of virus cases in the United States is just short of 3.5 million, according to Johns Hopkins University.
COVID-19 cases have been surging in the United States, particularly in states that were among the first to reopen and lift restrictions designed to halt the spread of the highly contagious virus.
As cases began to rise in Florida, Mr DeSantis reimposed a ban last month on allowing bars to sell alcohol for on-site consumption.
But Mr DeSantis has not followed the lead of California and Texas, for example, and imposed new lockdown orders or made the wearing of masks mandatory in indoor spaces.
Mr Trump's Republican Party is to hold its presidential nominating convention in the Florida city of Jacksonville next month.
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