By Anne K Walters and Michael Donhauser

Des Moines, Iowa (dpa) - Hillary Rodham Clinton had a razor-thin margin early Tuesday over fellow Democrat Bernie Sanders for the Iowa caucuses, where the first votes were cast in the US presidential nomination process.

Among Iowa Republicans, conservative Senator Ted Cruz topped the field, with billionaire businessman Donald Trump finishing second and Senator Marco Rubio a close third.

Clinton and Sanders were nearly dead even, with Clinton at 49.9 per cent, and Sanders at 49.6 per cent, with 1,682 of 1,683 precincts reporting, the state Party said.

Clinton's campaign declared victory in what the party described as the "the closest in Iowa Democratic caucus history."

"Hillary Clinton has won the Iowa Caucus. After thorough reporting - and analysis - of results, there is no uncertainty and Secretary Clinton has clearly won the most national and state delegates," her campaign said.

"Statistically, there is no outstanding information that could change the results and no way that Senator Sanders can overcome Secretary Clinton's advantage," said Matt Paul, Clinton's Iowa state director.

Both Democrats addressed their supporters before the final result was certain, but it was clear they would effectively split Iowa's slate of delegates to the left-leaning party's convention.

Heading into the vote, speculation had swirled about whether former secretary of state Clinton could again lose in Iowa to an upstart challenger, after falling to Barack Obama in the 2008 caucus.

"It looks like we are in a virtual tie," Sanders declared, bringing a huge cheer from the crowd, which chanted "Bernie, Bernie."

"What Iowa has begun tonight is a political revolution," said Sanders, who serves in the Senate as an independent and identifies as a democrat socialist, in a country where the term has become largely anathema.

Clinton stopped short of declaring victory, telling supporters earlier in the night: "As I stand here tonight, breathing a big sigh of relief - thank you, Iowa."

Cruz won 27.7 per cent of the vote to Trump's 24.3 per cent, with 99 per cent of precincts reporting, the Iowa Republican Party said.

Florida Senator Marco Rubio was in a close third place with 23.1 per cent, better than opinion polls had indicated ahead of the first hurdle for candidates seeking to rise to the nation's highest elected office.

Both Sanders and Cruz painted the results as victories over their parties' political establishments, as well as special interests and the media, though they have nearly diametrically opposed policy positions.

Cruz, a first-term senator from Texas who has frequently clashed with his party's leaders, declared his victory a win for "courageous conservatives."

He vowed to focus on changing business in Washington, declaring a "victory for millions of Americans who have shouldered the burden of seven years of Washington bargains run amok" under Obama.

Cruz relied on extensive get-out-the-vote efforts to push him ahead of Trump, who had run an unconventional campaign marked by large rallies but had been plagued by questions about whether his supporters would actually vote.

Trump, who has played up his outsider status in vitriolic rants against the political establishment, his opponents and the media, vowed to fight on in the next contest next week in the north-eastern state of New Hampshire and eventually come out on top nationwide.

"We will go on to get to the Republican nomination, and we will easily go on to beat Hillary or Bernie, or whoever the hell they throw up there," Trump told supporters after losing to Cruz, who had trailed Trump in opinion surveys going into the vote.

Rubio's stronger than expected result could secure his status as the favoured candidate among the Republican establishment, which opposes Cruz as a disagreeable hardliner and sees Trump as an outside usurper.

"When I am our nominee, we are going to unify this party, and we are going to unify the conservative movement," Rubio said.

He vowed to expand the conservative party's appeal to people struggling economically, "and bring them to our side."

Many of the 11 Republican and three Democratic candidates had held rallies and shook hands across the rural Midwestern state into the final hours before the Monday night caucuses, but some, including former Florida governor Jeb Bush, had already turned their attention to the next contest, the New Hampshire primary on February 9.

For decades, Iowa has been first to vote in the state-by-state nominating process leading up to this year's national party conventions in July. The general election is November 8.

The Iowa contest traditionally winnows down the field of candidates, and as results rolled in, Democrat Martin O'Malley and Republican Mike Huckabee, who received few votes in Iowa, both quit the race.