WASHINGTON: Kamala Harris and Donald Trump return to the campaign trail Thursday, with the Democrat hoping her dominant display in their first presidential debate will boost her chances in the knife-edge US election.

The rivals are heading to crucial battleground states that will decide November's vote, two days after Harris forced Republican Trump onto the defensive in a fiery clash that drew 67 million viewers across the United States.

But it remains unclear whether the vice president's punchy performance will turn the dial with less than two months to go in an agonisingly tight race that will be decided by a handful of undecided voters across the country.

Harris, 59, will seek to capitialise on her debate momentum as she heads to North Carolina on Thursday, holding back-to-back rallies in the cities of Charlotte and Greensboro promising a "new way forward."

Harris has erased a six-point Trump lead over the last month to draw level in North Carolina, where she is aiming to fire up crucial Black and young voters to back her bid to become America's first woman commander in chief.

Amid media reports of turmoil in his camp over the way Harris succeeded in goading him at the debate, the 78-year-old former president is due onstage in Tucson, Arizona to focus on "our struggling economy."

Arizona was one of the most bitterly fought states in the 2020 election, with Joe Biden winning there by around 10,000 votes against Trump, and promises to be closely contested again.

Their return to the swing states at the heart of the election came a day after a brief truce when they attended Wednesday's anniversary of the 9/11 attacks in New York.