Progressive US Senator Bernie Sanders has won the Democrats’ New Hampshire presidential primary vote – declaring a victory for his campaign after the bungled Iowa primary.

There was a thunderous roar from the packed crowd at the Southern New Hampshire University field house where Mr Sanders delivered his election victory speech when he took the stage.

“This victory here is the beginning of the end for Donald Trump … With victories behind us – the victory tonight in New Hampshire and last week in Iowa – we’re going to Nevada, we’re going to South Carolina. We’re going to win those states as well,” he said after declaring victory.

The result is significant for Mr Sanders, who outpaced Pete Buttigieg, the moderate former Indiana mayor, and Senator Amy Klobuchar, who was looking for a breakthrough after a strong debate performance on Friday.

Our victory tonight is the beginning of the end for Donald Trump.

— Bernie Sanders (@BernieSanders) February 12, 2020

But it was a blow for former frontrunner Joe Biden, who came a dismal fifth in New Hampshire following a lacklustre fourth in Iowa. A deflated Mr Biden reportedly skipped his planned New Hampshire primary-night party ahead of another expected loss, and flew to South Carolina for further campaigning.

However, he hopes to stay in the race until the February 29 contest in South Carolina and a series of contests in other Southern states on Super Tuesday on March 3, where his support among African Americans will be a strength.

“It ain’t over, man. It’s just getting started,” Mr Biden said in South Carolina.

Votes were still being counted on Wednesday afternoon (Australian time). But CNN reported that – with just over 70 per cent of results counted – these were the positions:

1. Bernie Sanders (26.1 per cent)
2. Pete Buttigieg (24.1 per cent)
3. Amy Klobuchar (20 per cent)
4. Elizabeth Warren (9.3 per cent)
5. Joe Biden (8.5 per cent)
6. Tom Steyer (3.6 per cent)

Elizabeth Warren, a progressive ally of Mr Sanders who was considered a favourite in New Hampshire three months ago, also had a bad night.

She will face questions about her continued viability after her fourth-place finish.

Results in New Hampshire began rolling in quickly after polls closed, and local Democrats were confident they would have smoother sailing than in Iowa, where embarrassing technical problems delayed vote-counting and the release of results for days.

Mr Buttigieg narrowly beat Mr Sanders in Iowa, but both campaigns have asked for a partial recanvass of the results.

The results began to thin the field of Democrats seeking the right to take on Mr Trump, with businessman Andrew Yang and Senator Michael Bennet dropping out after it became clear they would finish well out of the running.

CBS News reported that Deval Patrick, the former Massachusetts governor, would drop out on Wednesday.

Meanwhile, Mr Trump has easily won the Republicans’ primary in New Hampshire, against minimal opposition.

Mr Trump was declared the winner as polls in the state closed on Tuesday night (local time).

Four years ago, the state offered Mr Trump his first primary victory and helped catapult him to the White House.

-with AAP