Americans were voting on Tuesday under the shadow of a surging coronavirus pandemic to decide whether to reelect Republican Donald Trump, one of the most polarising presidents in US history, or send Democrat Joe Biden to the White House.

A record-breaking number of early votes — some 100 million — have already been cast in an election that has the country on edge and is being closely watched in capitals around the world.

The 77-year-old Biden, who served for eight years as vice president to Barack Obama, leads Trump in national polls and in many of the battleground states that will decide the White House.

The former senator from Delaware, who is making his third bid for the presidency, began his day with a visit to the church in Wilmington, Delaware, where his son, Beau Biden, and first wife and daughter are buried.

Trump, 74, who is seeking to become the first US president to win reelection after being impeached, dismissed the polls showing him trailing Biden.

"I think we have a very solid chance of winning," he said Tuesday morning on "Fox and Friends". "We think we're doing very well everywhere. The crowds have been incredible."

"Our country can never be the same country if they win," Trump said, adding that America would become a "socialist" nation.

At the same time, Trump has cast doubt on the integrity of the election and threatened legal challenges, claiming the only way he can lose is if the results are "rigged".

Casting her vote in New York, Megan Byrnes-Borderan, 35, said Trump's threats were "part of why it is so scary".

"I believe that Trump will go through all odds to try to win the election,” she said.

Trump has waged a campaign against mail-in voting for months, claiming it could lead to fraud and all ballots should be tabulated on Election Day.

Several states, including battlegrounds Michigan, Pennsylvania and Wisconsin, do not begin counting mail-in ballots until Election Day itself.

‘Done with the chaos!’ 

Besides the White House, all 435 seats in the House of Representatives are at stake, and Democrats are expected to hold and possibly expand their majority in the chamber.

Roughly one-third of the Senate is up for grabs and Republicans risk losing their 53-47 majority.

The bitter divisions and passions sparked by the bruising election campaign are sure to leave one side disappointed and have sparked fears of unrest.

In Washington and many other cities, stores have been boarding up and law enforcement is on high alert.

In a tweet flagged with a warning label by Twitter, Trump said a slow vote count in crucial Pennsylvania could lead to "rampant and unchecked cheating”.

"It will also induce violence in the streets. Something must be done!” he tweeted.

Biden has focused his attacks on Trump’s handling of the Covid-19 pandemic which has left more than 231,000 people dead in the United States, and the divisive nature of his presidency.

"We’re done with the chaos! We’re done with the tweets, the anger, the hate, the failure, the irresponsibility,” Biden said at an election eve rally in Cleveland, Ohio.

"We’re coming together for a big win tomorrow,” Biden said in Pittsburgh, Pennsylvania, where he was joined by pop superstar Lady Gaga. "It’s time to stand up and take back our democracy.”

Biden, like Hillary Clinton in 2016, is expected to win the popular vote but all eyes are on the 538-member Electoral College that ultimately determines the winner of the race.

A candidate needs 270 electoral votes to win and it may come down to voters in the tossup states of Arizona, Florida, Georgia, Michigan, North Carolina, Ohio and Pennsylvania.

Trump won 306 electoral votes in 2016 and he predicted on Tuesday he would do even better this time. "I think we’ll top it,” he said.

Trump, who was briefly knocked off the campaign trail in early October by a bout with Covid-19, wrapped up his campaign with a whirlwind day of rallies, addressing supporters twice in Michigan and making stops in North Carolina, Pennsylvania and Wisconsin.

He ended up in the early hours of Tuesday in Grand Rapids, Michigan — the same place where he concluded his against-the-odds campaign in 2016.

‘How could he not win?’ 

While Tuesday is formally Election Day, in reality Americans have been voting for weeks.

With a huge expansion in mail-in voting to safeguard against the Covid-19 pandemic, some 100 million people have already made their choice.

Trump has lost ground among suburban women, who favour Biden by a double-digit margin, and his "law and order” response to protests for racial justice may have turned off many Black voters.

Trump’s handling of the coronavirus pandemic has also led to a potential loss of support among seniors.

In one of US history’s great political gambles, Biden stuck to socially distanced gatherings with small crowds while Trump held large rallies where few supporters wore masks.

Many early votes are believed to have been cast by Democrats, and Trump’s side is hoping for a massive wave of Republican supporters voting in person on Tuesday.

"When you come to one of these rallies, all you think is, how could he not win?” said Kolleen Wall, who turned out to cheer Trump in Grand Rapids.

As voters went to the polls in the US, the eyes of the world were on the fate of a norm-breaking president with the campaign slogan "America First”.

Trump’s first term featured strained relations with NATO allies, withdrawal from the Paris climate accord and World Health Organisation and renunciation of the Iran nuclear deal.

Relations with China have also become increasingly strained with Trump blaming Beijing for the Covid-19 pandemic.