The two rivals, who have forcefully attacked each other on the campaign trail, mostly struck a cordial tone on Tuesday, instead saving their fire for the candidates at the top of their tickets, Democratic Vice President Kamala Harris and Republican former president Donald Trump.

The most tense exchange occurred near the end of the debate, when Vance - who has said he would not have voted to certify the results of the 2020 election - avoided a question about whether he would challenge this year's vote if Trump loses.

Walz responded by blaming Trump's false claims of voter fraud for instigating the January 6, 2021, mob that attacked the US Capitol in an unsuccessful effort to prevent the certification of Joe Biden's 2020 election.

"He is still saying he didn't lose the election," Walz said, before turning to Vance.

"Did he lose the 2020 election?"

Vance again sidestepped the question, instead accusing Harris of pursuing online censorship of opposing viewpoints.

"That is a damning non-answer," Walz said.

Walz, 60, the liberal governor of Minnesota and a former high school teacher, and Vance, 40, a bestselling author and conservative firebrand US senator from Ohio, have portrayed themselves as two sons of America's Midwestern heartland with deeply opposing views on the issues gripping the country.

The rivals each sought to land a lasting blow at the last remaining debate before the November 5 presidential election, arguing over the Middle East crisis, immigration, taxes, abortion, climate change and the economy.

But by and large the two men appeared intent on providing a demonstration of "Midwestern nice," thanking each other even while they went after their respective running mates in the traditional attack-dog role for vice presidential candidates.