Donald Trump told supporters Monday he is "not a Nazi," using a rally in the final week of a bitter White House race to disprove accusations of authoritarianism, including from a former top aide who branded him a fascist.

As he and rival Kamala Harris, the current vice president, entered the final stretch of one of the closest US elections in modern times, each candidate and their teams have ramped up the political rhetoric, inflaming an already tense campaign.

Democrat Harris, who has accused Trump of stoking divisions, crisscrossed Michigan on Monday while the Republican visited Georgia, another of the decisive swing states, where he said critics are accusing him of being a modern-day "Hitler."

"The newest line from Kamala and her campaign is that everyone who isn't voting for her is a Nazi," Trump told a boisterous rally in Atlanta.

"I'm not a Nazi. I'm the opposite of a Nazi."

The comments come a day after Trump held a major rally in New York's famed Madison Square Garden that was widely condemned for racist remarks his allies made during the event.

They also follow the recent publication of a New York Times interview in which Trump's longest-serving White House chief of staff, retired general John Kelly, said the Republican fits the definition of a fascist — something Harris said she agreed with last week.

Kelly also said Trump had remarked that "Hitler did some good things too" and that he "wanted generals like Adolf Hitler had."

'Dividing our country' 

Tensions are soaring in a race polls suggest is too close to call, fueled by fears that former president Trump could again refuse to recognise a defeat, as in 2020, and by his harsh rhetoric threatening migrants and political opponents.

On Monday, a fire reportedly consumed hundreds of early ballots cast in a supposedly secure drop-off box in a competitive district in northwestern Washington state.

Another ballot box was damaged hours earlier in Portland, Oregon, where police said in a statement that an "intentional act" of arson sought to "impact the election process."

Trump has faced renewed outrage after one of the warm-up speakers at his Sunday rally in New York called US territory Puerto Rico "a floating island of garbage."

Harris, aiming to become the country's first female president, slammed "that nonsense last night at Madison Square Garden" as she spoke to reporters before boarding Air Force Two on Monday.

"He is focused and actually fixated on his grievances, on himself, and on dividing our country. And it is not in any way something that will strengthen the American family, the American worker."

Later in Ann Arbor, Michigan, at a rally with her running mate Tim Walz and a crowd of around 20,000, she described how "so much is on the line" on November 5.

"Donald Trump is even more unstable and more unhinged, and now he wants unchecked power."

His campaign said the Puerto Rico comments did "not reflect the views of President Trump."

Residents of the island cannot vote in presidential elections, but those within the United States proper — which includes about 450,000 Puerto Ricans in crucial battleground Pennsylvania — can.

A top Harris surrogate, former president Barack Obama, was in Philadelphia Monday rallying her supporters — and assailing Trump's allies for "trotting out and peddling the most racist, sexist, bigoted stereotypes."

He also appealed to Pennsylvania voters with Puerto Rican ties, saying: "If somebody does not see you as fellow citizens with equal claims to opportunity, to the pursuit of happiness, to the American dream, you should not vote for them."

'Nasty' 

Trump used Sunday's event — likened by Democrats to an infamous 1939 rally of American fascists in the same venue — to lash out on familiar topics including undocumented migrants and domestic opponents whom he again branded the "enemy from within."

And in Atlanta, he reprised his attacks on Harris, calling her a "hater," and said former first lady Michelle Obama was "nasty" for criticising him.

More than 47 million Americans have already cast ballots in early voting — including outgoing President Joe Biden, who voted Monday near his hometown of Wilmington, Delaware.

As the clock ticks down, the challenge for Harris and Trump is both to energise core supporters and pull in the tiny number of persuadable voters who might still tip the balance — especially in the seven swing states where polls have them running neck-and-neck.

On Tuesday, Harris will deliver what her campaign calls a "closing argument" from the same spot near the White House where then-president Trump stoked his supporters on January 6, 2021, to launch a violent assault on the US Capitol.