President Trump again hinted that a vaccine might be available before the November presidential election and accused his Democratic rivals of “reckless anti-vaccine rhetoric”.
Mr Biden expressed scepticism that Mr Trump would listen to the scientists and implement a transparent process.
The virus has also claimed nearly 190,000 lives and fuelled a major recession, double-digit unemployment and sagging consumer confidence.
Last week it emerged the US Centers for Disease Control and Prevention (CDC) had urged states to consider “waiving requirements” in order to be able distribute a vaccine by 1 November – two days before the 3 November election.
No vaccine has yet completed clinical trials, leading some scientists to fear politics rather than health and safety is driving the push for a vaccine.
Both Mr Biden and his running mate Kamala Harris have questioned the president’s credibility on the issue. Ms Harris said on Sunday she would not trust Mr Trump’s word that a vaccine was safe, and Mr Biden also questioned whether the wider public would trust him too.
“He has said so many things that aren’t true I am worried that if we do have a really good vaccine people are going to be reluctant to take it,” Mr Biden said in Pennsylvania on Monday, Labour Day.
But he added that: “If I could get a vaccine tomorrow, I’d do it. If it cost me the election I would do it. We need a vaccine and we need it now. We have to listen to the scientists.”
Mr Trump, who is trailing in the polls, hit back at a White House news conference, calling Mr Biden “stupid” and Ms Harris “the most liberal person in Congress… not a competent person in my opinion”.
He said they “would destroy this country and would destroy this economy”, and added that they “should immediately apologise for the reckless anti-vaccine rhetoric that they are talking right now”.
The president, at times asking journalists to take off their face masks when asking questions, again suggested a vaccine could be ready next month.
“We’re going to have a vaccine very soon, maybe even before a very special date,” he said.
The top US infectious diseases expert, Dr Anthony Fauci, has said that it is unlikely but “not impossible” that a vaccine could win approval in October, and Stephen Hahn of the Food and Drug Administration said it might be “appropriate” to approve a vaccine before clinical trials are complete if the benefits outweighed the risks.
But both scientists, the White House and the executives of five top pharmaceutical companies have made clear there will be no compromises on safety and effectiveness of a vaccine.
Three vaccine trials in the US are in their final stages – each involving 30,000 people who will get shots, three weeks apart, and will then be monitored for coronavirus infections and side effects for anywhere from a week to two years, the Associated Press reports.