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 has stood by and pushed the Trump campaign message of "law and order" and has remained a vigorous defender of police. In an interview with ABC News Live Anchor Linsey Davis, Pence said that he and Trump "reject the notion from Joe Biden and others that there's an 'implicit bias' towards minorities in law enforcement."

"The president and I know we don't have to choose between supporting law enforcement and supporting all of the families that live in our major cities," Pence told a crowd of supporters in Lititz, Pennsylvania. "We have done both for the last three and a half years, and we're going to support law enforcement and support our African American and minority families for four more years in the White House."

The vice president has dismissed the "defund the police" movement and has called for more resources and better training and accountability in law enforcement.

On matters of racial discrimination in policing and use of force, Harris has called for the rooting out of racial discrimination. In the aftermath of George Floyd's killing while in police custody she participated in protests in Washington, D.C.

During an appearance on ABC's "The View" in June, Harris was asked by co-host Meghan McCain if she supports the "Defund the Police" slogan, but did not give a direct answer on where she stands.

"We need to re-imagine how we are achieving public safety in America. And to have cities where one-third of their entire budget is going to policing but yet there's a dire need in those same cities for mental health resources, for resources going into public schools, for resources going into job training and job creation. Come on. We have to be honest about this that there isn't a consensus around this because if there were, we would actually see a smarter distribution of resources in our country to address the issues that need to be addressed."

After the shooting by police of Jacob Blake, she met with Blake's family in Wisconsin and spoke with Blake over the phone. She also told NBC News, "I think that there should be a thorough investigation, and based on what I've seen, it seems that the officer should be charged." She's also kept in contact with Tamika Palmer, the mother of Breonna Taylor who was shot by Louisvill, Kentucky, police while she was sleeping in her home.

Harris has called for economic and educational investment in communities of color to create safer, healthier communities. She and Biden have called for an end to no-knock warrants, chokeholds and carotid holds. They want to create a national excessive force standard and create a database to track cops who use excessive force and break the rules. The pair want to end cash bail and private prisons.

"We have to understand that you can't think that the only way to create safe communities is to put more police on the streets, that's not how it's going to work," Harris told pop star Lizzo on an Instagram Live stream in September.

In contrast, Harris wrote in her 2009 book "Smart on Crime," "if we take a show of hands of those who would like to see more police officers on the street, mine would shoot up."

-ABC News' Justin Gomez and Averi Harper