Philadelphia, Pennsylvania - Kamala Harris and Donald Trump made their final case Monday in the hours before Election Day, when voters will either choose America's first woman president or hand the Republican a comeback likely to rattle the world.

With polls showing a dead heat, Trump promised to lead the US to "new heights of glory" while Harris said the "momentum is on our side," as the rivals held their last rallies of the 2024 race in crucial battleground states.

The Democratic vice president finished in Philadelphia in the must-win state of Pennsylvania, with a rally on the steps immortalized by the boxing movie Rocky.

"This could be one of the closest races in history – every single vote matters," said Harris, who was joined by celebrities including Lady Gaga and Oprah Winfrey.

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She also referenced the film, telling thousands of supporters that "here at these famous steps" she was paying "tribute to those who start as the underdog and climb to victory."

Harris (60) has repeatedly said she is the underdog, having only joined the race three months ago after President Joe Biden dropped out. But she insisted she would win.

Former president Trump brought several family members – with the conspicuous absence of his wife Melania – up on stage at his closing rally in Grand Rapids, Michigan.

There, as in an earlier swing through North Carolina and Pennsylvania, his speech bristled with dark rhetoric.

"With your vote tomorrow, we can fix every single problem our country faces and lead America – indeed, the world – to new heights of glory," he told the crowd, as the clocks ticked over into Tuesday.

The candidates' final pitches reflected the critical importance that turnout is likely to play in a nail-biting race.

Both sides say they are encouraged by early turnout, with more than 82 million people having cast early ballots – but they now need to mobilize supporters on Election Day itself.

A charged-up Trump said his supporters can "put ourselves in a position to win, which we can do very easily if we show up."

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Harris said, "We need everyone to vote in Pennsylvania and you will decide the outcome."

Polls open on the East Coast at 6:00 AM Tuesday – although in the tiny New Hampshire hamlet of Dixville Notch they opened at the stroke of midnight, recording three votes for Trump and three for Harris.

In the final days, the Republican and Democrat have delivered sharply contrasting messages.

Speaking earlier in Reading, Pennsylvania, Trump pursued his racist rhetoric about a US in decline and overwhelmed by immigrants without documentation, whom he described as "savages" and "animals."

Harris, meanwhile, hammered home her opposition to Trump-backed abortion bans across the US – one of her key vote-winning positions.

She also called for a "fresh start" after nearly a decade of Trump dominating US political discourse.

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But despite being tarred with criminal convictions and the scandal of his supporters' violent attack on Congress four years ago, when he refused to accept the results of the 2020 election, he goes into Election Day with major advantages.

Trump has pressed home on voter concerns about the economy and the border, making repeated and baseless accusations about migrants.

His message struck home for first-time voter Ethan Wells, a 19-year-old restaurant cook in Michigan.

Biden "let a lot of illegals in, and they've been murdering and raping our own people," he claimed to AFP. "When Trump was president, nobody messed with America."

Harris has had to build an entire campaign in three months, but she has quickly galvanized the Democratic Party.

"Tomorrow, we will elect the first female president," Luke Little, a 24-year-old server, said in Philadelphia.

The world is anxiously watching as the outcome will have major implications for Israel's wars in the Middle East and Russia's war in Ukraine, and for tackling climate change, which Trump calls a hoax.

The most immediate fear is that US democracy will be tested if Trump loses but refuses to accept defeat like he did four years ago, when his supporters stormed the US Capitol.

With Trump having narrowly survived an assassination attempt in July and police foiling a second alleged plot, the fears of violence are very real.

In Washington, growing numbers of businesses and office buildings are being boarded up in case of unrest.