Des Moines, Iowa: Donald Trump, who told his supporters that under his leadership the United States would win so much that they would get sick of winning, has lost the Iowa caucuses to hard-right senator Ted Cruz, and barely held off the challenge of Marco Rubio for second place.

Hillary Clinton, who came third in Iowa eight years ago before losing the Democratic nomination to Barack Obama, was being declared the winner by a nose in an incredibly tight contest with socialist senator Bernie Sanders.

With about 99 per cent of the vote counted Ted Cruz, a firebrand senator from Texas who is as much of an insurgent against his own party as Trump, led 28 per cent to 24 per cent.

Marco Rubio, a conservative freshman senator from Florida seen as more closely aligned with the party establishment, defied expectations to secure 23 per cent of the vote.

The strong showing leaves him as the strongest hope for that establishment to regain control of a party which has been divided and bewildered by the Trump and Cruz campaigns.

The results fly in the face of polling, which had given Trump a five per cent lead over Cruz as recently as Saturday.

Introduced as "the next president of the United States", Trump addressed a crowd in an Iowa conference centre a little before 11pm, saying he had been warned last year that he could never even make "the top 10" in Iowa.

He told hundreds of relatively subdued supporters that he loved Iowa. "You're very special. I think I might come back here and buy a farm."

Cruz's victory and Rubio's strong showing appear to reinforce the importance of carefully organised grassroots campaigns which can identify potential supporters and encourage them to get out and vote, even in the face of a media juggernaut like Trump's.

The results also thinned the ranks of contenders, with the Democrat Martin O'Malley, who polled one per cent, and the Republican former governor of Arkansas, Mike Huckabee, both calling an end to their campaigns before counting was formally finished.

The results in Iowa set the scene for coming votes in New Hampshire, South Carolina and Nevada.

Rubio will now be able to urge establishment donors who early in the race had supported Jeb Bush, who captured just 2.8 per cent of the vote, to transfer their support to him.

New Hampshire is expected to be far kinder to Trump as well. It has far fewer evangelical voters - who have so far been suspicious of Trump's religious conviction - and a voting system that demands less commitment than the Iowa caucuses.

On the Democratic side, Sanders is expected to easily defeat Clinton in New Hampshire, given his profile as the senator for neighbouring Vermont.

But Clinton is expected to reassert her strength as the race then moves to southern states.