The early results on Tuesday were expected, with the race likely to come down to seven battleground states: Georgia, North Carolina, Arizona, Michigan, Nevada, Pennsylvania and Wisconsin.
Opinion polls showed the rivals neck-and-neck in all seven going into election day.
Nearly three-quarters of voters say American democracy is under threat, according to preliminary national exit polls from Edison, reflecting the nation's deep anxiety after a contentious campaign.
An Edison Research poll shows 73 per cent of voters believe democracy is in jeopardy. (AP PHOTO)
Democracy and the economy ranked by far as the most important issues for voters, with about a third of respondents citing each, followed by abortion and immigration.
The poll shows 73 per cent of voters believed democracy is in jeopardy against 25 per cent who say it's secure.
The data underscores the depth of polarisation in a nation where divisions have only grown starker during a fiercely competitive race.
Trump employed increasingly apocalyptic rhetoric while stoking unfounded fears that the election system cannot be trusted.
Harris warned a second Trump term would threaten the underpinnings of American democracy.
Hours before polls closed on Tuesday, Trump claimed on his Truth Social site without evidence that there was "a lot of talk about massive CHEATING" in Philadelphia, echoing his false claims in 2020 that fraud had occurred in large, Democratic-dominated cities.
There is absolutely no truth to this allegation. It is yet another example of disinformation. Voting in Philadelphia has been safe and secure. — Seth Bluestein (@SethBluestein) pic.twitter.com/wMiPnAgO17November 5, 2024
In a subsequent post, he also asserted there was fraud in Detroit.
"I don't respond to nonsense," Detroit City Clerk Janice Winfrey told Reuters.
A Philadelphia city commissioner, Seth Bluestein, replied on X: "There is absolutely no truth to this allegation. It is yet another example of disinformation. Voting in Philadelphia has been safe and secure."
Trump, whose supporters attacked the US Capitol on January 6, 2021, after he claimed the 2020 election was rigged, voted earlier near his home in Palm Beach, Florida.
"If I lose an election, if it's a fair election, I'm gonna be the first one to acknowledge it," Trump told reporters.
His campaign has suggested he might declare victory on election night even while millions of ballots have yet to be counted, as he did four years ago.
Donald Trump voted near his Florida home, saying he would respect the result of a "fair" election. (AP PHOTO)
The winner might not be known for days if the margins in battleground states are as slim as expected.
Millions of Americans waited in orderly lines to cast ballots, with only sporadic disruptions reported across a handful of states, including several non-credible bomb threats that the FBI said appeared to originate from Russian email domains.
Trump planned to watch the results at his Mar-a-Lago club before speaking to supporters at a nearby convention centre.
Harris, who had previously mailed her ballot to her home state of California, spent some of Tuesday in radio interviews encouraging listeners to vote.
Later, she was due to address students at Howard University, a historically Black college in Washington where Harris was an undergraduate.
"To go back tonight to Howard University, my beloved alma mater, and be able to hopefully recognise this day for what it is, is really full circle for me," Harris said in a radio interview.
Kamala Harris spent election day doing radio interviews and imploring people to vote. (AP PHOTO)
A dizzying race churned by unprecedented events - two assassination attempts against Trump, President Joe Biden's surprise withdrawal and Harris's rapid rise - remained too close to call after billions of dollars in spending and months of frenetic campaigning.
No matter who wins, history will be made.
Harris, 60, the first female vice-president, would become the first woman, Black woman and South Asian American to win the presidency.
Trump, 78, the only president to be impeached twice and the first former president to be criminally convicted, would also become the first president to win non-consecutive terms in more than a century.
Control of both chambers of Congress is also up for grabs. Republicans have an easier path in the US Senate, where Democrats are defending several seats in Republican-leaning states, while the House of Representatives looks like a toss-up.
