Trump tweeted in support of Pence saying he is, "doing GREAT" and Harris, calling her a "gaffe machine," a criticism he uses often to attack her running mate Joe Biden.

Biden has also tweeted in support of his running mate during the debate, saying that Harris is "showing the American people why I chose her as my running mate."

In speaking to American leadership, Pence brought up the case of Kayla Mueller, a humanitarian worker from Arizona who was kidnapped by the Islamic State in Syria in 2013 and died in the terror group's custody.

Mueller's parents were in the debate's audience as Pence's guests and appeared last month at the Republican National Convention.

Pence suggested former President Barack Obama and Biden carried blame for Mueller's death, saying they "hesitated for a month" while she was held captive.

Harris, in her response to the topic of American leadership, first addressed Mueller's family.

"First of all, to the Mueller family, I know about your daughter's case and I'm so sorry. I'm so sorry. What happened to her is awful and it should have never happened," Harris said. "And I know Joe feels the same way. And I know that President Obama feels the same way."

In a discussion of foreign policy and the role of American leadership, Harris brought up Trump’s handling of the Iran nuclear deal and criticized the president's “unilateral” approach.

“He's walked away from agreements,” she said. “We were in the Iran nuclear deal with friends, with allies around the country. And because of Donald Trump's unilateral approach to foreign policy, coupled with his isolationism, he pulled us out and has made America less safe.”

“So, Susan, it's about relationships and the thing that has always been part of the strength of our nation, in addition to our great military, has been that we keep our word,” she added. “But Donald Trump doesn't understand that because he doesn't understand what it means to be honest.”

On the issue of jobs, Harris took aim at the Trump administration trade policy with China.

“You lost that trade war. You lost it. What ended up happening is because of a so-called trade war with China, America lost 300,000 manufacturing jobs,” Harris said. “Farmers have experienced bankruptcy because of it. We are in a manufacturing recession because of it.”

Pence responded by criticizing Joe Biden’s record on China, calling him, “a cheerleader for communist China.”

“When Joe Biden was vice president, we lost 200,000 manufacturing jobs and President Obama said they were never coming back,” Pence said.

HARRIS' CLAIM: "Joe Biden has been so incredibly transparent, and certainly by contrast, the president has not. Both in terms of health records, but also let's look at taxes. We now know because of great investigative journalism that Donald Trump paid $750 in taxes. When I first heard about it, I literally said, you mean $750,000? And it was like, no, $750. We now know Donald Trump owes and is in debt for $400 million."

PENCE'S CLAIM: "The president said those public reports are not accurate and the president's also released literally stacks of financial disclosures the American people can review just as the law allows."

FACT CHECK: As a presidential candidate in 2016 and as a sitting president since, Donald Trump has released annual financial disclosure reports filed to the Federal Election Commission and the Office of Government Ethics, as required by federal laws. Trump's annual personal financial records, which are nearly 100-pages each, show his source of income, other assets, as well as liabilities.

Trump, however, has not released his personal tax records, which is not required by law but has been a decades-long tradition that has been followed by his predecessors in the White House.

Biden and Harris have differentiated themselves from Trump by releasing their federal and state tax returns -- most recently just last week, showing Biden and his wife paid roughly $290,000 in taxes to the federal government in 2019, and Harris and her husband paid about $1.2 million in federal and state taxes last year.

Harris' claim that Trump paid just $750 in taxes comes from The New York Times' recent report. According to the Times, Trump's tax records show that he paid just $750 in federal income taxes the year he ran for president and his first year in the White House.

The report also stated that Trump is personally responsible for loans and other debts totaling $421 million, "with most of it coming due within four years."

--ABC News' Soorin Kim