Donald Trump leads Kamala Harris in all swing states as US ...

Republican nominee Donald Trump had claimed some swing states and was leading Democratic rival Kamala Harris in all others as counting in the US presidential election extended into Wednesday morning, local time.

Both candidates dominated in their traditional heartlands, and as the night went on, Trump began pulling ahead in the key battlegrounds.

The Associated Press called the first of seven swing states for Trump — North Carolina — just after 3:15pm on Wednesday AEDT. 

He later flipped Georgia.

By 1:30am local time (5:30pm AEDT), he was within striking distance of the White House.

Many analysts predict the election will go down to the wire, and be among the closest in the country's history.

In the final week of the campaign, multiple polls predicted Harris, the US vice president, was enjoying a late surge of support among voters in multiple critical swing states.

However, when it came to counting the actual votes, those projections did not translate.

Just before 1am Wednesday local time (5pm AEDT), Harris's campaign manager strode out onto the stage at Washington DC's Howard University and told Democrats supporters their candidate would not be speaking that night.

On a buoyant night for the Republicans, not only did Trump appear set for another four years in the White House, but they also looked like having a majority in the Senate after winning seats off the Democrats.

A Donald Trump supporter watches the count at the Palm Beach County Convention Center in Florida. (Reuters: Brian Snyder)

In the US, each state runs voting in its own way. In some states, paper ballots are used while others have electronic voting machines.

Polls close at different times depending on where you are in the country, and votes are counted in distinct ways.

It means that if the result is close, a final tally may not be known for several days.

Most eyes are on five critical swing states yet to be called: Arizona, Wisconsin, Michigan, Nevada and Pennsylvania.

It became clear as the night progressed that Harris needed to win the so-called "blue wall" of Michigan, Pennsylvania and Wisconsin, although she trailed in all of them.

A man packs away a polling booth in Kalamazzoo, Michigan on Tuesday night. (Reuters: Carlos Osorio)

Under the US presidential election system, different states carry different numbers of electoral college votes, and the successful presidential candidate must reach at least 270.

The first polling places closed at 6pm on Tuesday (10am Wednesday AEDT), the last ones shut at 4pm AEDT.

After a frenetic week of campaigning across swing states, often hitting several in one day, both candidates decamped for a quieter day as the country voted.

Republican nominee Donald Trump, with his wife Melania, at his campaign headquarters on election day. (Reuters: Brian Snyder)

Earlier on Tuesday, local time, Harris used a radio interview broadcast in the battleground state of Georgia to encourage people to vote, saying her and Trump had "different visions of the future of our nation".

Trump, meanwhile, cast his vote at Florida's Mandel Recreation Centre on Tuesday, and told reporters he felt "very confident" of victory.

"It looks like Republicans have shown up in force," he said.

He is holding a watch party at Mar-a-Lago in Palm Beach, Florida.

Authorities were on high alert in multiple parts of the country as results came in.

In the capital city, Washington DC, temporary fences provided extra security around key government buildings, including the White House.

The insurrection on January 6, 2021 — the escalation of Trump's refusal to accept his 2020 presidential election loss — is still very much in the city's consciousness.

Elsewhere, people have been warned not to intimidate or attack workers or voters at polling places.

On Monday evening, Larry Krasner, the Pennsylvania district attorney, warned people not to "f*** around" with the election.

"We do have the cuffs, we do have the jail cells," he said.

Despite the preparations, voting took place amid relative calm around the country.

In Georgia, polling was interrupted at several polling places after bomb threats. A judge later ruled the affected locations could stay open later.