Republican presidential nominee Donald Trump was projected to win three states - Indiana, Kentucky and West Virginia - while Democratic candidate Hillary Clinton secured Vermont, as polls began closing late Tuesday in the United States.

The very early results gave Trump 24 votes in the electoral college to three for Clinton.

Each state's value is weighted by population in the electoral college, where a majority of 270 is needed to clinch the White House.

Among the hard-fought swing states that will decide the presidential race, North Carolina, Ohio and Virginia were already finished voting. Polls were due to close at 8 pm (0100 GMT) in Florida, New Hampshire and Pennsylvania.

Clinton and Trump earlier joined voters nationwide in voting after a long and bitter campaign.

Clinton entered election day with a narrow lead in most nationwide surveys of likely voters and was the favourite to win based on the state-by-state electoral college.

She cast her vote in Chappaqua, New York, where she and her husband, former president Bill Clinton, have lived since they left he White House in 2001.

"So many people are counting on the outcome of this election and what it means for our country, and I'll do the best I can if I'm fortunate enough to win today," she said.

Trump and his Slovenian-born wife, Melania, a naturalized citizen, cast their ballots at the polling station nearest their penthouse in Trump Tower in New York City.

When asked by reporters if he would accept unfavourable election results, Trump responded: "We'll see what happens," the Los Angeles Times reported.

Trump, whose populist rhetoric and inflammatory tweets dominated the campaign since he declared his candidacy in June 2015, last month refused to say he would concede defeat if the count goes against him.

People on the street outside the polling site shouted "loser" and booed the candidate from behind a police barrier. Others shouted "Go, Donald" and gave him thumbs up.

Trump, who for months was not taken seriously by the Republican establishment, has struggled to consolidate the conservative party's base.

Attracted by his populist hostility to immigrants and trade, many of his core supporters are drawn from disaffected white independents, who compared to the entire US population are older, less educated and disproportionately male.

At a polling station in Williamsburg in New York City's Brooklyn borough, Jasmin Stein said she felt some good had come of the divisive campaign.

"A lot of things have been coming to the light that I think the country feels, ... and I kind of would rather have it out in the open than it just be in peoples' homes," the 29-year-old said.

Jessica Quinn, 37, who brought her 8-month-old daughter to the polls, said she got so anxious about the elections that she volunteered to work for the Clinton campaign on Monday, making about 30 phone calls.

"I needed to do something productive with all of my anxiety about what was happening with the election," Quinn said.