When confronted by Wallace about the disparity between what his public health officials are saying and what he has said about the timing of the vaccine, Trump stuck with his previous comments.

"We can have it a lot sooner," Trump said. "It's a very political thing because people like this would rather make it political than save lives."

Top U.S. government public health officials and other experts have said that it's possible -- if everything goes well, but unlikely -- that vaccine trials will have enough clear and compelling data to be available by the end of October or beginning of November. Dr. Anthony Fauci, the nation's foremost infectious disease expert, has said he thinks there will be a "safe and effective vaccine" by "the end of this calendar year."

Fauci has also said that the United States will not return to "normal" until the middle of next year.

Biden interrupted the president by referring to Trump's previous statements earlier this year, when he said the virus would be gone by Easter and then also referenced Trump's potentially dangerous comment that people can inject bleach to get rid of the virus. Trump then responded that he said the bleach comment "sarcastically" made.

Biden turned to the hundreds of thousands of Americans who have died due to the coronavirus.

"His own head of the CDC said if we just wore masks between now -- if everybody wore masks and social distanced -- between now and January, we probably save up to 100,000 lives," Biden said.

Wallace pivoted the conversation to the global COVID-pandemic, and Biden began by listing statistics including 200,000 Americans dead and over 7 million infected.

"The president has no plan. He hasn't laid out anything. He knew all the way back in February how serious this crisis was. He knew it was a deadly disease," Biden said. "And I laid out again in July what we should be doing."

You should get out of your bunker and get out of the sand trap and your golf course and go in your Oval Office and bring together the Democrats and Republicans and fund what needs to be done now to save lives," he continued.

Trump countered by saying if the country had listened to Biden then millions of people would have died, not 200,000, and touted his decision to restrict travel from China in February, along with his efforts on ventilators and vaccine development.

"When you talk about numbers you don't know how many people died in China, you don't know how many people died in Russia, you don't know how many people died in India. They don't exactly give you a straight count," Trump said.

While on the topic of the Supreme Court and the fate of the Affordable Care Act, Trump was quick to call Biden's health care plan "socialized Biden."

Biden, notably, has said he does not support "Medicare for All" and responded by calling out Trump for promising to repeal and replace Obamacare -- which he hasn't.

"He does not have a plan," Biden said. "The fact is this man doesn't know what he's talking about."

Less than 20 minutes into the debate, both candidates have interrupted each other multiple times, making it difficult to understand what either is saying. Wallace has specifically asked Trump multiple times to let Biden finish his thought.

Eventually, the cross-talks continued for long enough that the former vice president said, "Will you shut up, man?" to the president.

Russia's ongoing brazen efforts to interfere in the presidential election -- as they did four years ago -- remains a principal concern among national security officials, along with other adversaries including China. But unlike in 2016, the rapid and sweeping embrace of vote-by-mail in response to the coronavirus pandemic injects new uncertainty about election security, as millions prepare to vote in an alternative way.

Fueling those anxieties over mail voting, which is underway in several states, is President Trump’s unsubstantiated allegations of rampant fraud, even as dozens of state election officials tell ABC News that they have confidence in the system. His campaign against vote-by-mail throughout the cycle exceeds similar efforts he made in 2016, when he argued, without evidence, that voter fraud was the only reason Hillary Clinton won the popular vote. His own voting integrity commission found no evidence of that.

The integrity of this year's matchup between Trump and former Vice President Joe Biden has taken on an outsized role in the increasingly competitive political environment, as attempts to undermine confidence in the democratic process mount both from outside the country's borders and from inside the Oval Office.

Biden has attempted to combat Trump’s onslaught by pointing out that Trump himself has voted-by-mail in Florida from the White House.

Some elections experts argue Trump’s offensive against mail-in voting is a voter suppression tool, which could lay the "groundwork for contesting a close election if he loses, " wrote Rick Hasen, a professor of law and political science at the University of California, Irvine, and the author of "Election Meltdown: Dirty Tricks, Distrust and the Threat to American Democracy."

"The most benign explanation for Mr. Trump’s obsessive focus on mail-in balloting is that he is looking for an excuse for a possible loss to his Democratic opponent, Joe Biden, in November. The less benign explanation is that he is seeking to sow chaos to drive down turnout and undermine the legitimacy of the election," wrote Hasen,.

At the first presidential debate on Tuesday at Case Western Reserve University in Cleveland, Ohio, the two rivals are set to spar over the integrity of the election, one of the topics previewed by the Commission on Presidential Debates.

Here's what we know about the candidates' histories with and stances on the issue

-ABC News' Kendall Karson and Quinn Scanlan