Republican Donald Trump has claimed victory over Democrat Kamala Harris in the US presidential election, capping a stunning political comeback four years after he left the White House.

Fox News projected Trump had won the presidency, although other media outlets were yet to call the race.

“America has given us an unprecedented and powerful mandate,” he said early on Wednesday to a roaring crowd of supporters at the Palm Beach County Convention Centre.

Trump thanked the American people for “being elected the 45th and 47th president.”

“This will be the golden age of America. This is a magnificent victory for the American people that will allow us to make America great again.”

He also spent several minutes praising Elon Musk, the richest man in the world, who pumped some $US120 million into backing Trump’s campaign. Trump has said he will appoint Musk to lead a government efficiency commission.

Other news outlets had yet to call the race for Trump, but he appeared on the verge of winning after capturing the battleground states of Pennsylvania, North Carolina and Georgia and holding leads in the other four, according to Edison Research.

Harris did not speak to her supporters, who had gathered at her alma mater Howard University. Her campaign co-chair, Cedric Richmond, briefly addressed the crowd after midnight, saying Harris would speak publicly on Wednesday.

“We still have votes to count,” he said.

The former president was showing strength across broad swaths of the country, improving on his 2020 performance everywhere from rural areas to urban centres.

Republicans also won a US Senate majority after flipping Democratic seats in West Virginia and Ohio.

Neither party appeared to have an edge in the fight for control of the House of Representatives where Republicans currently hold a narrow majority.

Trump went into election day with a 50-50 chance of reclaiming the White House, a remarkable turnaround from January 6, 2021, when many pundits pronounced his political career over.

That day, a mob of his supporters stormed Congress in a violent attempt to overturn the results of the 2020 election.

Trump picked up more support from Hispanics, traditionally Democratic voters, and lower-income households that have keenly felt the sting of price rises since the last presidential election in 2020, according to exit polls from Edison.

Voters whose top issue was the economy voted overwhelmingly for Trump, especially if they felt they were worse off financially than they were four years ago.

About 31 per cent of voters said the economy was their top issue, and they voted for Trump by a 79 per cent-to-20 per cent margin, according to exit polls.

Some 45 per cent of voters across the country said their family’s financial situation was worse off today than four years ago, and they favoured Trump 80 per cent to 17 per cent for Harris.

At Howard University, where a large watch party was being held for Harris, supporters were leaving in droves, anticipating that the vice president would not address the crowd on Tuesday night.

Cedric Richmond, a co-chair of the Harris campaign, briefly addressed the crowd and said Harris would not speak.

“We still have votes to count,” he said.

“We still have states that haven’t been called yet.”

Trump was earning a bigger share of the vote than he did four years ago in almost every corner of the country, from suburban Georgia to rural Pennsylvania.

By 11pm US eastern time, officials had almost completed their count of ballots in more than 1200 counties – about a third of the country – and Trump’s share was up about 2.0 percentage points compared to 2020, reflecting a broad if not especially deep shift in Americans’ support for the president they ousted four years ago.

He had improved his numbers in suburban counties, rural regions and even some large cities that are historically bastions of Democratic support.

In Florida, a ballot measure that would have guaranteed abortion rights failed to reach the 60 per cent threshold needed to pass, according to Edison, leaving a six-week ban in place.

Nine other states have abortion-related measures on the ballot.

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.

He was watching the results at his Mar-a-Lago club – reportedly joined by Tesla CEO Elon Musk – before speaking to supporters at a nearby convention centre, according to sources familiar with the planning.

Tuesday’s vote capped a dizzying race churned by unprecedented events, including two assassination attempts against Trump, President Joe Biden’s surprise withdrawal and Harris’ rapid rise.

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.