Pete Buttigieg and Bernie Sanders took the lead as the first results in the Iowa Democratic caucus were finally released, a day after technical issues caused chaos.
With 62 per cent of results released, Mr Buttigieg, the former mayor of South Bend, Indiana, was leading the field on state delegate equivalents, with Vermont senator Mr Sanders second.
In the popular vote their positions were reversed.
Elizabeth Warren, the Massachusetts senator, was third in both, followed by former vice-president Joe Biden and Amy Klobuchar, the Minnesota senator, in fifth.
The partial results were announced as the chairman of the Iowa Democratic Party, Troy Price, apologised for the problems which have inspired mockery from Donald Trump and others.
Mr Price promised an independent investigation into what happened, saying: "We've been working day and night to make sure these results are accurate."
Speaking to supporters in Laconia, New Hampshire, after the early results were announced, Mr Buttigieg said he had begun the race a year ago with four staff members, no name recognition and no money, but with "a big idea".
The Afghanistan veteran has argued it is time for a new generation of leaders in the party and that his lack of experience in Washington makes him an ideal candidate to break the partisan gridlock in the nation's capital.
He said: "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."
Officials blamed the embarrassing hold-up on inconsistencies related to a new mobile app used for vote.
Iowa is the first electoral test in the presidential calendar, although some Democrats have long complained that the largely white farm state has an outsized role in determining the party's nominee.
Mr Trump took a swipe at the Democrats, 11 of whom are contenders in the state-by-state battle to face him in November. "Nothing works, just like they ran the Country," he tweeted.
Before the Iowa results were released, campaign aides for Mr Biden cited gross failures in the caucuses.
"What we're saying is there are some inconsistencies, that the process, the integrity, is at stake. And the Iowa Democratic Party needs to check that data, check it again, check it a third time, check it a fourth time, because it's important to get it right," campaign senior adviser Symone Sanders.
Reuters contributed to this report
