After a long and exceptionally negative campaign, millions of Americans voted on Tuesday for their next president as opinion polls showed Democrat Hillary Clinton with a narrow lead over Republican Donald Trump.

In a battle focused on the character of the candidates, Clinton, 69, a former U.S. secretary of state, and Trump, 70, a New York businessman, accused each other of being unfit to lead the United States against challenges like an arduous economic recovery, Islamist militants and the rise of China.

As he did during the campaign, Trump on Tuesday raised the possibility of not accepting the election's outcome, saying he had seen reports of voting irregularities. He gave few details and Reuters could not immediately verify the existence of such problems.

"We're going to see how things play out today. Hopefully they'll play out well and hopefully we won't have to worry about it, meaning hopefully we'll win," the former reality TV star said in a telephone interview on Fox News. "I want to see everything honest."

Trump also sued the registrar of voters in Nevada's Clark County over a polling place in Las Vegas that had been allowed to remain open late last week during an early voting period to accommodate people, many of them Hispanic, who were lined up to cast ballots.

Clinton, aiming to become the first woman U.S. president, cast her ballot at an elementary school near her home in Chappaqua, New York early on Tuesday morning.

"It is the most humbling feeling. I know how much responsibility goes with this. So many people are counting on the outcome of this election, what it means for our country. And I'll do the very best I can if I'm fortunate enough to win today," Clinton said.

Trump, in his first bid for elected office, received a mixture of cheers and jeers as he arrived to vote at a school in Manhattan.

Clinton led Trump, by 44 per cent to 39 per cent, in the last Reuters/Ipsos national tracking poll before Election Day.

A Reuters/Ipsos States of the Nation poll gave Clinton a 90 percent chance of defeating Trump and said she was on track to win 303 Electoral College votes, with 270 needed for election.

Financial markets, betting exchanges and online trading platforms largely predicted a Clinton win, although Trump's team says he can pull off an upset victory like the June "Brexit" vote to pull Britain out of the European Union.

Trump's candidacy embodied an attack on America's political establishment. Clinton represented safeguarding the political order.

A Clinton presidency would likely provide continuity from fellow Democrat Barack Obama's eight years in the White House, although if Republicans retain control of at least one chamber in Congress more years of political gridlock in Washington could ensue.

A win for Trump could shake some of the basic building blocks of American foreign policy, such as the NATO alliance and free trade, and reverse some of Obama's domestic achievements such as his 2010 healthcare law.

Polls will begin to close at 7 p.m. ET, with the first meaningful results due about an hour later. U.S. television networks called the winner of the 2008 and 2012 presidential elections at 11 p.m. ET or shortly after.

Victory in U.S. presidential elections is earned not by the popular vote, but by an Electoral College system that awards the White House on the basis of state-by-state wins, meaning a handful of states where the race is close assume an outsized importance.

Majorities of voters in opinion polls viewed both candidates unfavorably after a marathon campaign that began in early 2015.

"They're both not good candidates, but I'd rather vote for 'worse' than 'worser,'" said Estefani Rico, 20, a first-time voter who cast her ballot for Clinton at a library in Miami. "It's nerve racking that in my first time being able to vote I get the worst candidates ever," she said.

Mary Wheeler, 94, held her nose when asked which candidate she was supporting as she stood in line to vote at the Coliseum ballroom in St. Petersburg, Florida, an important battleground state.

"I always vote Republican, so I guess I'll do that," Wheeler said. "He can make a fool of himself but I think he may be able to straighten things out a little bit," she said of Trump.

Trump and Clinton were seeking to succeed Democrat Obama, who served two four-year terms in the White House and is barred by the U.S. Constitution from seeking another term.

Clinton spent eight years in the White House as U.S. first lady, the wife of President Bill Clinton, from 1993 to 2001 before serving as a senator and as Obama's secretary of state. She also ran for president in 2008, but lost to Obama for the Democratic nomination.

Trump has vowed to crack down on illegal immigration and end trade deals he says are harming U.S. workers.

Trump seized the spotlight time and again during the campaign with provocative comments about Muslims and women, attacks against the Republican establishment and bellicose promises to build a wall along the U.S. southern border with Mexico to stem illegal immigration.

The Dow Jones Industrial Average index closed at 18,332.43, up 72.83 points (0.4 per cent) as investors bet on a win for Clinton, who Wall Street sees as more likely to ensure financial and political stability. Mexico's peso hit a two-month high on Tuesday on the expectation of a loss for Trump, who has vowed to rip up a trade deal with Mexico.

The NASDAQ closed with a 0.53 per cent gain, adding 27.31 points to settle at 5,193.49. The S&P/TSX Composite (up 4.39 points to close at 14,656.84) and the S&P 500 (up 8.01 to close at 2,139.53) also finished the day in the green.

Trump was expected to draw support heavily from white voters without college degrees.

Clinton was likely to draw support from college-educated voters and Hispanic and black voters.

Major bookmakers and online exchanges were confident Clinton would win. Online political stock market PredictIt put her chances on Tuesday of capturing the White House at 80 per cent.

Trump advisers say the level of his support is not apparent in opinion polls and point out that the real estate developer has been closing the gap with Clinton in surveys in recent weeks.

MUST-WIN STATES

An early indicator of who might prevail could come in North Carolina and Florida, two must-win states for Trump that were the subject of frantic last-minute efforts by both candidates.

Races in both those states were shifting from favoring Clinton to being too close to call, according to opinion polls.

Democrats also are seeking to break the Republican lock on control of the U.S. Congress.

A strong turnout of voters for Clinton could jeopardize Republican control of the Senate, as voters choose 34 senators of the 100-member chamber on Tuesday. Democrats needed a net gain of five seats to win control. All 435 seats in the House of Representatives are being contested. The House is expected to remain in Republican hands.

Trump reveled in the drama of the negative presidential campaign but the spotlight was not always kind to him. The release in October of a 2005 video in which he boasted about groping women damaged his campaign and left him on the defensive for critical weeks

Clinton, with a long reputation for secrecy, sustained damaging blows from her handling of classified information as the country's top diplomat. It was only two days before the election that FBI Director James Comey reiterated that she would not face criminal charges.

Trump's vice presidential running mate is Mike Pence, the governor of Indiana. Clinton's running mate is U.S. Senator Tim Kaine of Virginia.