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.

PENCE'S CLAIM: "It's probably why Newsweek magazine said that Kamala Harris was the most liberal member of the United States Senate in 2019, more liberal than Bernie Sanders, more liberal than any of the others in the United States Senate."

FACT CHECK: Harris certainly has a very liberal Senate voting record, and an analysis cited by Newsweek in 2019 did find her to be the most liberal in the U.S. Senate.

However, that particular analysis does not consider some important caveats, the founder of the organization who conducted it told ABC News.

, an independent and nonpartisan group, found that Harris was the "most liberal" of her Senate colleagues in a 2019 survey, which compared the number of bipartisan bills a senator co-sponsored to the total number of bills he or she signed onto. Harris had the smallest percent of bipartisan bills in 2019, making her the most-liberal senator by this metric.

Harris certainly has one of the more liberal voting records in the Senate: She has voted to increase gun control and block conservative judicial nominees, for instance.

But there are nuances that the organization's founder, Jonathan Tauberer, said GovTrack's model doesn't account for, like the complexity of Harris' political views, the distinctions between different wings within each major political party, the specific approach Harris might take to achieve her desired outcome, or the unwillingness of Republicans to work with Harris during a presidential year.

--ABC News' Allison Pecorin