US Democratic presidential candidates Pete Buttigieg and Bernie Sanders were neck and neck late on Thursday with 100 percent of precincts reporting in the chaotic Iowa caucuses.

The tally comes hours after the Democratic party chairman ordered a review of the results following technology problems in the United States's first nominating contest and some doubts were raised about the accuracy of the process.

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Sanders, the progressive senator from Vermont, and Buttigieg, the former mayor of South Bend, Indiana, are separated by a razor-thin margin in the latest batch of results.

Democratic Party chairman Tom Perez, however, stepped in earlier on Thursday, demanding a review of the results from Monday's caucuses.

"Enough is enough," Perez said on Twitter. "In order to assure public confidence in the results, I am calling on the Iowa Democratic Party to immediately begin a recanvass."

With returns in from all of the 1,765 precincts in Iowa, Buttigieg was leading by 26.2 percent to Sanders's 26.1 percent in the delegate totals.

Massachusetts progressive Senator Elizabeth Warren was next with 18.0 percent, followed by former Vice President Joe Biden with 15.8 percent and Minnesota Senator Amy Klobuchar with 12.3 percent.

Buttigieg, Sanders declare themselves winners

Earlier in the day, Buttigieg declared himself the winner based on the number of delegates from the Midwestern state who will be sent to the Democratic convention in July while Sanders claimed victory based on the popular vote.

"It has been an extraordinary week, and we are absolutely electrified ... by the extraordinary validation of this campaign's vision that we had in Iowa," Buttigieg told military veterans and other voters on Thursday at American Legion Post 98 in Merrimack, New Hampshire.

He also turned an eye towards the state's primary vote, to be held on Tuesday.

"So I know in the days leading up to primary day it is my responsibility to seek to earn every vote in a state that famously thinks for itself, in a state that lives by the motto of 'Live Free or Die'."

Democratic presidential candidate and former South Bend, Indiana, Mayor Pete Buttigieg speaks during a campaign stop at Community Oven in Hampton, New Hampshire [Brendan McDermid/Reuters]

Sanders, speaking on Thursday in nearby Manchester, pointed to his lead in Iowa's actual vote totals.

"In other words, some 6,000 more Iowans came out on caucus night to support our candidacy than the candidacy of anyone else," he said.

"From where I come from, the person who gets the most votes wins," Sanders said, arguing that too much emphasis was being put on delegate totals.

At the end of the day, he said, the caucus system is "much, much, much too complicated" and it was a mistake for the state party to "rely on untested technology".

Party officials have blamed the technical meltdown on a "coding error".

Democratic presidential candidate Senator Bernie Sanders speaks during a campaign rally [Steven Senne/AP Photo]

President Donald Trump pounced on the debacle in the first-in-the-nation contest to decide which Democrat faces him in November.

"The Democrat Party has given up on counting votes in Iowa. Looks like it all got computer 'fried'," Trump tweeted on Friday.

"Iowa and New Hampshire will not be moved from the Primary Schedule as long as I am President," he added, apparently referring to growing calls for the schedule to be adjusted so that a state that is more representative of the US kicks off the nominating contests.

"Great tradition," he said.

Buttigieg appeared to be getting a bounce from his strong Iowa performance as the latest New Hampshire poll showed the centrist candidate in second place in the state.

The Boston Globe/WBZ-TV/Suffolk University poll had Sanders, who won the New Hampshire primary four years ago before eventually losing the nomination to Hillary Clinton, topping the field with 25 percent.

Buttigieg's support surged to 19 percent from 12 percent on Monday, according to the poll, while Biden saw his backing slide over the same period.

Sanders, Buttigieg, Biden, Warren, Klobuchar, businessman Tom Steyer and entrepreneur Andrew Yang will face off on the debate stage in New Hampshire on Friday night.

'Gut punch'

Biden, the national frontrunner who described his likely fourth-place finish in Iowa as a "gut punch", met his advisers on Thursday to map out a strategy.

"I expected to do better," Biden, 77, said as he launched attacks on rivals.

"If Senator Sanders is the nominee for the party, every Democrat in America ... will have to carry the label Senator Sanders has chosen for himself," Biden said of the self-described democratic socialist.

Biden, who served in the Senate for 36 years before becoming Barack Obama's vice president, said 38-year-old Buttigieg's lack of experience was "a risk" for Democrats.

The Sanders campaign announced, meanwhile, that it had raised $25m in January, its largest fundraising month yet.

After New Hampshire, the candidates turn their sights on Nevada on February 22, South Carolina on February 29 and then the March 3 "Super Tuesday", when 14 states hold primaries.