"I would use all that energy and I would put that towards more supply of the vaccine," Mr DeSantis said at a news conference over the weekend.
His answer was in response to reports that Mr Biden directed the Federal Emergency Management Agency (FEMA) to open 100 government vaccination sides nationwide.
At the White House press briefing on Monday, Jen Psaki, the press secretary, was asked about Mr DeSantis’ criticism and what the president thought about it.
“The president is a pretty even-keeled guy, so I would say he doesn’t have much of a reaction other than he wants to ensure the vaccine is distributed to people across the country, including, of course, the millions of people living in Florida,” she said.
She went on to criticise the Republican governor, given how his state has only distributed about 50 per cent of its current vaccine supply.
“I will note because we're data first here, facts first here, they’ve only distributed about 50 per cent of the vaccines they have been given in Florida. So clearly they have a good deal of the vaccine, that supply will need to continue to increase as they are able to effectively reach people across the state,” she added.
The Covid-19 plan, which was released last week, had several aspects to it about how the federal government would develop a nationwide mass vaccination campaign, such as increasing manufacturing and supply, as Mr DeSantis suggested.
This included Mr Biden issuing an executive order that directs “relevant agencies to exercise all appropriate authorities, including the [Defense Production Act], to accelerate manufacturing, delivery, and administration to meet shortfalls in equipment and supplies needed for the Covid-19 response".
Relevant agencies would be responsible for producing Personal Protective Equipment (PPE), such as gowns and masks, as well as necessary equipment to ramp up Covid-19 testing and vaccine manufacturing.
While speaking in Jacksonville on Monday, Mr DeSantis updated the vaccine numbers in Florida. The state has received about 1.7 million first doses of the Covid-19 vaccine, and has distributed those first doses to 1,224,188 people,” he said.
"When you look at it from the perspective of the first doses, we've done a very high percentage of them, and we continue to go even higher," he continued.
Mr DeSantis said there were “unused” vaccine doses, but most of them were being held for people to receive the second dose of his vaccine.
His numbers contradicted those reported by the CDC, which claimed that Florida has received more than 2.9 million doses of the vaccine. Despite this, Mr DeSantis used his press conference to again implore the federal government to focus on sending supplies versus building vaccination centres, claiming his state was moving doses faster than it was receiving them.
"We don't have a big cache sitting around at the state. We only get what they send us. The sole focus for the federal government should be increasing the number of doses available for the states," Mr DeSantis said. "We were told weeks ago that we would start to see increases now and we've haven't seen it. We've been very stagnant this whole month."
Florida received 266,000 doses from the federal government last week, he added. But the governor wanted closer to 500,000 doses each week to bump up vaccinations.
"If we can get 500,000 a week, instead of just 266,000, we're gonna be able to vaccinate that many more seniors that much more quickly," he continued. "We're at the mercy of what the federal government sends us."
The Biden administration inherited a Covid-19 plan from the Trump administration that was "much worse than we could have imagined,” Ms Psaki said during her press briefing.
"We are assessing now what we have access to, and ensuring that we have more of a rapid engagement with states so that they have more of a heads up on what to expect in the weeks ahead," she added.