Pete Buttigieg and Bernie Sanders are leading in the first vote to choose the Democratic candidate to run against President Donald Trump in November's election.
The vote in Iowa has been chaotic, beset by technical problems and delays in reporting results.
Iowa's Democratic Party said data from 71% of precincts showed Mr Buttigieg on 26.8%, with Mr Sanders on 25.2%.
Elizabeth Warren was third on 18.4% and Joe Biden fourth on 15.4%.
Amy Klobuchar was on 12.6%, and Andrew Yang on 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. Democrats have blamed the delay on a coding error with an app being used for the first time to report the votes.
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 nominee 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.
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.
In the popular vote count, partial results showed Mr Sanders leading with 32,673 ballots, while Mr Buttigieg was second at 31,353.
However, Mr Buttigieg came top in certain rural areas with smaller populations, and so far has more delegates.
Ms Warren was third with 25,692, followed by Mr Biden at 16,447 and Ms Klobuchar at 15,470.
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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.
The app was developed by tech firm Shadow Inc., run by veterans of Hillary Clinton's failed 2016 presidential campaign.
It was put together in just two months and had not been independently tested, the New York Times reported, quoting people briefed on the matter by the Iowa Democratic Party.
The party in Nevada, where caucuses will be held on 22 February, has reversed a decision to use the company's software.
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".
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.
We finally have some 2020 Iowa caucuses results to talk about. And they're going to generate a lot of talk - and hand-wringing.
There are clear winners, as Bernie Sanders and Pete Buttigieg can both claim some kind of victory, depending on how the final tabulations come in.
There's also a clear loser - Joe Biden. He entered Monday leading in some polls and hoping for a strong showing that would put to bed concerns that he is a flawed front-runner.
Instead those concerns are wide awake and pacing the room.
Unlike candidates like Mr Sanders, Elizabeth Warren and Mr Buttigieg, the Biden campaign coffers are thin - and this Iowa performance isn't opening any cash spigots.
It could have been worse for the former vice-president - he could have had to give a fourth-place concession speech on Monday night - but the end result is the same.
He was unable to land a knock-out blow on fellow moderate Amy Klobuchar, while Mr Buttigieg and Mr Sanders both exit Iowa strengthened, suggesting Mr Biden could be staring at a third-place finish - or worse - in New Hampshire.
Until proven otherwise, Biden still has his southern-state firewall, based on support from elderly and black voters. But the flames are licking at his heels.
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."