Iowa's Democratic Party said data from 62% of precincts showed Mr Buttigieg on 26.9% with Mr Sanders on 25.1%.

Elizabeth Warren was third on 18.3% and Joe Biden fourth on 15.6%.

The eventual nominee will challenge President Donald Trump, a Republican, in November's White House election.

Amy Klobuchar was on 12.6%, and Andrew Yang on 1.1%, according to the other preliminary results released on Tuesday evening from all of Iowa's 99 counties. Tom Steyer and Tulsi Gabbard were on less than 1%.

But the state party has still not declared a winner from Monday's vote, which was derailed by technical malfunctions.

The results represent the share of delegates needed to clinch the party nomination under America's quirky political system. Iowa awards only 41 of the 1,991 delegates required to become the Democratic White House nominee.

But in the popular vote count, partial results showed Mr Sanders leading with 28,220 ballots, while Mr Buttigieg was second at 27,030.

Ms Warren was third with 22,254, followed by Mr Biden at 14,176 and Ms Klobuchar at 13,357.

A simple guide to US primaries and caucuses

Iowa was the first contest in a string of nationwide state-by-state votes, known as primaries and caucuses, that will culminate in the crowning of a Democratic White House candidate at the party convention in Milwaukee, Wisconsin, in July.

Eleven candidates remain in a Democratic field that has already been whittled down from more than two dozen.

Where did it all go wrong?

Iowa Democratic party chairman Troy Price told a news conference on Tuesday evening the fiasco had been "simply unacceptable".

"I apologise deeply for this," he added of the turmoil, which has provoked calls for Iowa to lose its coveted spot atop the presidential voting calendar.

"This was a coding error," he said, while insisting the data was secure and promising a thorough review.

State party officials earlier said the problem was not the result of "a hack or an intrusion".

Officials were being dispatched across the Hawkeye state to retrieve hard-copy results.

They were matching those numbers against results reported via a mobile app that many precinct captains said had crashed.

Trump declares 'win' amid Democratic caucus chaos

Voters flocked on Monday to more than 1,600 caucus sites, including libraries, high schools and community centres.

President Trump said earlier that the Iowa Democratic caucuses had been an "unmitigated disaster".

Who is Pete Buttigieg?

If elected, 38-year-old Mr Buttigieg would be the first openly gay US president.

He is the former mayor of South Bend, Indiana, a city of just over 100,000 people.

He is a former Harvard and Oxford University Rhodes scholar, who served as a military intelligence officer in Afghanistan and used to work for global management consultancy McKinsey.

Rivals say Mr Buttigieg, who is younger than Macaulay Culkin and Britney Spears, is too inexperienced to be US president.

But he says he is transformative outsider who can break the gridlock in Washington and defeat President Trump.

Campaigning in Laconia, New Hampshire, on Tuesday evening, Mr Buttigieg welcomed the preliminary results.

"A campaign that started a year ago with four staff members, no name recognition, no money, just a big idea, a campaign that some said should have no business even making this attempt, has taken its place at the front of this race to replace the current president with a better vision for the future," he said.

How have the other campaigns responded?

After pumping nearly $800m (£610m) into campaigning in Iowa, the rival campaigns expressed dismay at the debacle.

Mr Sanders, a Vermont senator, told reporters he was "obviously disappointed" at the hold-up, which he said was "not a good night for democracy".

He said there was no reason to cast "aspersions" on the results, but criticised Mr Buttigieg's decision to declare victory on Monday night, despite the lack of any official results.

"I don't know how anybody declares victory before you have an official statement from the election results, we're not even declaring victory," Mr Sanders said.

Ms Warren, a Massachusetts senator, and former US Vice-President Biden earlier on Tuesday questioned the state party's decision to release partial results.

Biden campaign senior adviser Symone Sanders told reporters: "What we're saying is there are some inconsistencies, that the process, the integrity, is at stake."