New York (AFP) - Kamala Harris and Donald Trump set out Wednesday to ride the momentum from their high-stakes debate into the final sprint to November as they seek to persuade undecided voters and shake up a presidential election locked in a dead heat.

The Democratic vice president and her Republican rival are neck-and-neck in both nationwide and swing state polling, days before first ballots are mailed out and early in-person voting begins in several key states.

Both candidates declared victory in the debate after coming face to face for the first time on the biggest night so far of the campaign – although any boost or dent in support is unlikely to show up in polling for several days.

The ABC News-hosted debate in Philadelphia was punctuated by tense exchanges, although Harris focused on policy while Trump’s answers were littered with wild falsehoods and were often about his past grievances.

On Wednesday, Trump came out swinging in an early morning interview with Fox News, claiming – without providing evidence – that the debate was “rigged” against him.

“It was a rigged deal, as I assumed it would be, because when you looked at the fact that they were correcting everything and not correcting with her,” he complained.

Observers said both candidates would have positives to take from the clash.

“She focused on the major thematic contrasts between her and Trump…. For his part, Trump didn’t hurt himself with his loyal followers but he likely didn’t make any inroads with undecided voters either,” said Andrew Koneschusky, a former press secretary to Democratic Senate leader Chuck Schumer.

Republican strategist Liam Donovan said Harris scored points on Trump, and the Republican “largely whiffed” in his efforts to tie his opponent to President Joe Biden’s more unpopular policies, instead “going on angry tirades about migrants run amok.”

“Don’t expect this debate to have an immediate impact in the polls, but it will surely boost morale at a time when Democrats are getting anxious,” he told AFP.

After replacing Biden as the candidate in July, Harris rode a wave of enthusiasm through the Democratic convention that boosted her popularity and gave her record fundraising numbers.

And with Biden gone, 78-year-old Trump finds himself as the candidate facing questions about his advanced age, with renewed focus on his eccentric and often rambling speeches.

But Harris, 59, had seen her polling momentum begin to stall ahead of the debate.

- The Trump base -

The Democrat has been reaching to the center, showcasing a parade of anti-Trump Republicans – most recently former vice president Dick Cheney and his daughter Liz, who was thrown out of the House leadership over her opposition to the tycoon.

Trump has been largely appealing to his own base, with apocalyptic warnings about migrant criminals and painting a dark picture of a country in “decline” that only he can save.

In a threatening social media post at the weekend, Trump vowed to prosecute Democratic donors, lawyers and elections officials who engage in behavior he deems “unscrupulous” in November.

He used the debate on Tuesday to double down on his bogus voter fraud claims from 2020.

Trump and Harris crossed paths again Wednesday when they attended ceremonies marking the 23rd anniversary of the September 11, 2001 attacks by Al-Qaeda.

Harris heads Thursday to North Carolina – one of a handful of states expected to decide the election, where she has erased a six-point Trump lead to draw level.

Trump is due onstage in Tucson, Arizona on Thursday focusing on “our struggling economy and the rising cost of housing.”

Harris’s running mate Tim Walz will travel to Michigan and Wisconsin from Thursday to Saturday, as his Republican opposite number J.D. Vance deals with the fallout from another round of controversial remarks.

The Republican vice presidential nominee amplified a false claim Monday that Haitian immigrants are abducting and eating pets in Ohio.

In the debate, Trump repeated the bizarre claim, which has been debunked by local authorities.