Trump said his administration is "trying very hard" to locate the 545 children whose parents can't be located after being separated from their parents. However, the president also said that some of the children were brought to the U.S. by "coyotes" and "cartels."

He then pivoted to say that the Obama administration built the detention centers where many migrants are held.

"They had a picture in a certain newspaper, there was a picture of these horrible cages. They said look at these cages. President Trump built them," Trump said. "Then it was determined they were built in 2014. That was him. They built cages."

In a fiery response, Biden emphasized that the children came to the U.S. with their parents.

"Coyotes didn't bring them over, Biden said. "Their parents were with them. They got separated from their parents, and it makes us a laughingstock and violates every notion of who we are as a nation.

Welker asked about the Obama administration's failure to deliver on immigration reform. Biden said that it took too long to get the policy correct.

"It took too long to get it right. Took too long to get it right," he said. "I will be president of the United States, not vice president of the United States. And the fact is, I've made it very clear, within 100 days, I going to send to the United States Congress a pathway to citizenship for over 11 million undocumented people and all of those so-called dreamers, those DACA kids, they are going to be immediately certified again to be able to stay in this country and put on a path to citizenship."

Trump responded that Biden "had eight years to do what he said he was going to do."

Biden and Trump then went back and forth over the catch-and-release policy.

TRUMP'S CLAIM: "Nobody knew where it was coming from, what it was. We've learned a lot. But Anthony said don't wear masks. Now he wants to wear masks."

FACT CHECK: Dr. Anthony Fauci, one of the top infectious disease experts in the country, and other public health experts initially told Americans not to wear surgical or N95 masks in the early days of what has become the COVID-19 pandemic.

At the beginning of the pandemic, the Centers for Disease Control and Prevention and the World Health Organization, as well as Fauci and other top experts, initially discouraged wearing masks because of concerns that masks and other personal protective equipment were in short supply for health care workers who needed them. Public health officials were also concerned wearing masks could have unintended consequences if people touched their face more often to adjust them or fail to keep social distancing.

"There was this feeling that there would be a shortage just for those who really need them very early on," Fauci said in a recent interview. "That was the big deal. We didn't have enough PPE including masks. Then it became clear that cloth masks worked reasonably well. And therefore there was no more shortage. Then the different analyses, meta analyses and others came in that in fact, it does work."

In early April, the CDC changed its recommendation about face coverings for the general public, based on evidence that a significant number of people who were asymptomatic or not yet feeling sick were transmitting the virus.

Duke University researchers have also concluded that "if 95 percent of people wear cloth masks when within 6 feet of other people in public, it will reduce COVID-19 transmission by at least 30 percent."

Trump also said he thought Fauci was a Democrat, but Fauci is not registered as a member of any political party, according to D.C. voting records.

-ABC News' Stephanie Ebbs and Arielle Mitropoulos

TRUMP'S CLAIM: “When I closed, he said, 'This is a terrible thing. You're xenophobic.' I think he called me racist, even, and -- because I was closing it to China. Now, he says I should have closed it earlier. It just -- Joe, it doesn't work."

FACT CHECK: While Trump claimed that Biden opposed his decision to ban most travel from China at the outset of the coronavirus pandemic and that he called the restrictions "xenophobic," the former vice president did not explicitly weigh in on the decision when it was announced on Jan. 31. He did call the president xenophobic minutes after the partial travel ban was announced, but did not call Trump a racist for the decision.

During a campaign event that same day in Fort Madison, Iowa, Biden discussed the growing concern over the COVID-19 outbreak and cautioned that Trump should let science "lead the way."

"In moments like this, this is where the credibility of a president is most needed as he explains what we should and should not do," Biden told the crowd at the event. "This is no time for Donald Trump's record of hysterical xenophobia ... and fear-mongering to lead the way instead of science."

The comments came just minutes after the White House announcement, so it was unclear if Biden was referring to the decision specifically, but the former vice president did tweet a similar sentiment the next day.

"We are in the midst of a crisis with the coronavirus," Biden posted. "We need to lead the way with science -- not Donald Trump's record of hysteria, xenophobia, and fear-mongering. He is the worst possible person to lead our country through a global health emergency."

Throughout March, Biden used the word "xenophobic" in various speeches and tweets to criticize the president labeling COVID-19 as the "China virus."

Biden did acknowledge the travel restrictions put in place by the Trump administration in a March speech, noting they "may" slow the spread.

"Banning all travel from Europe or any other part of the world may slow it, but as we've seen, it will not stop it. And travel restrictions based on favoritism and politics rather than risk will be counterproductive," Biden said.

Biden's campaign did not explicitly discuss the vice president's view of the ban until April.

"Joe Biden supports travel bans that are guided by medical experts, advocated by public health officials and backed by a full strategy," Biden's deputy campaign manager Kate Bedingfield told CNN. "Science supported this ban, therefore he did too.

-ABC News' Molly Nagle

Welker turned her attention to the lingering stimulus discussions in Congress and asked Trump why he hasn't helped the millions of Americans who haven fallen into poverty, particularly minorities and women.

Trump laid the blame on House Speaker Nancy Pelosi.

"But you're the president," Welker contended.

"Nancy Pelosi does not want to approve it. We are ready, willing and able to do something," Trump said.

Biden, however, noted that Senate Majority Leader Mitch McConnell said he can not pass the stimulus bill because he doesn't have the votes.

When asked how he would work differently, the vice president said the Democrats have been pushing to pass the bill for the months.

"Look, they passed this act all the way back in the beginning of the summer. This is like -- it's not new. It's been out there," Biden said.

The final topic of the night was climate change with Welker first asking each candidate how he would combat climate change and support job growth at the same time as president. Trump answered first.

"So we have the trillion trees program. We have so many different programs. I do love the environment, but what I want is the cleanest, crystal clear water, the cleanest air," Trump said, taking credit for the country's reduced carbon emission last year.

He went on to slam other counties air-quality and tout the U.S. by comparison.

"Look at China, how filthy it is. Look at Russia. Look at India. It's filthy. The air is filthy. The Paris Accord, I took us out because we were going to have to spend trillions of dollars, and we were treated very unfairly," Trump said, closing his two minutes by saying his administration has done an incredible job "environmentally."

When it was Biden's turn, he pivoted to the existential threat he says global warming poses to humanity and said the U.S. has a moral obligation to "deal with it" -- but said climate change also creates a prime opportunity for new jobs.

"Here's where we have a great opportunity. I was able to get both all the environmental organizations as well as labor, the people worried about jobs, to support my climate plan. Because what it does -- it will create millions of new good-paying jobs," Biden said. "Wall Street firms indicated that my plan -- my plan will, in fact, create 18.6 million jobs, 7 million more than his. This is from Wall Street. And I'll create $1 trillion more in economic growth than his proposal does. Not on climate, just on the economy."

Trump slammed Biden's response, claiming the former vice president's plan would cause a massive economic depression and deeming it a "pipe dream," before raising Biden's stance on fracking.

In the face of Trump's criticisms, Welker asked Biden directly, "Would you rule out banning fracking?"

"I do rule out banning fracking," Biden said. "We need other industries to transition to get to ultimately a complete zero emissions by 2025. What I will do with fracking over time is make sure we can capture the emissions from the fracking, capture the emissions from gas. We can do that and we can do that by investing money. It's a transition to that."

"Excuse me," Trump interrupted. "He was against fracking. He said it. I will show that to you tomorrow."

"Fracking on federal land, I said," Biden responded. "No fracking and/or oil on federal land."