"Let me begin by stating that I imagine, have a strong feeling, that at some point the results will be announced," Sanders said to cheering supporters Monday night. "And when those results are announced I have a good feeling we're going to be doing very, very well in Iowa."

Data released late Monday by Sen. Bernie Sanders reflected 40% of precincts and appeared to show Buttigieg in second place, with about 26% share of state delegate equivalents, compared with about 29% for Sanders.

"So, we don't know all the results," Buttigieg told hundreds of supporters at a rally in Des Moines. "But, we know, by the time it is all said and done, Iowa you have shocked the nation. Because, by all indications, we are going on to New Hampshire victorious."

Democratic hopeful Pete Buttigieg declared victory in the Iowa caucuses early Tuesday, despite a botched election process that delayed the release of the state's results.

Senator Bernie Sanders, an independent from Vermont and 2020 presidential candidate, arrives to speak with his wife Jane Sanders during a caucus night watch party in Des Moines, Iowa, U.S. on Monday, Feb. 3, 2020.

The confusion was caused by a lack of official results in Monday's caucuses, the nation's first contest in the 2020 presidential race. The Iowa Democratic Party said late Monday that officials had found "inconsistencies" in the voting data and attributed the problem to a "reporting issue." The party said it had the underlying data and "will simply take time to further report the results."

In a statement early Tuesday, party Chairman Troy Price said the results were being verified manually and will be released later in the day.

In addition to Buttigieg and Sanders, other candidates including Sen. Amy Klobuchar of Minnesota projected confidence in their election night speeches, though Buttigieg went the furthest in predicting his own success.

A Buttigieg campaign aide told CNBC that data provided by 77% of the campaign's precinct captains showed Buttigieg in the lead. The campaign aide said that internal projections prior to the caucus suggested that the race would be a tie, but that the internal numbers so far showed Buttigieg performing 8 percentage points better than expected, enough to win first place.

Buttigieg told MSNBC on Tuesday that while official results have not been released, his campaign felt license to call it. "Unlike a primary where there's a secret ballot, this is folks standing in a room for all to see with their neighbors right there, with the press right there and with our own observers right there so it makes it possible for us to get a very clear sense of just how extraordinary a night it is," he said.

Officials working for other campaigns said that the data suggested a tight race, in line with polling conducted ahead of the caucus.

A data set released by the Sanders campaign, based on the results from 40% of Iowa precincts, showed the Vermont senator in the lead, followed by Buttigieg, Sen. Elizabeth Warren of Massachusetts and former Vice President Joe Biden. It showed Warren receiving about 18% share of state delegate equivalents and Biden receiving about 15%.

Roger Lau, Warren's campaign manager, told reporters only that according to the campaign's internal data it was a tight race between Warren, Buttigieg and Sanders. Biden lagged in fourth place, Lau said.

Klobuchar's campain manager, Justin Buoen, wrote in a post on Twitter that, based on internal numbers and public data, Klobuchar was tied with or ahead of Biden.

Buoen tweet

According to the Sanders data, Klobuchar was in fifth place, with about 11% share of state delegate equivalents.

The Biden campaign did not immediately respond to a request for comment. Campaign manager Greg Schultz tweeted a statement that said the campaign's model showed that the former vice president "overperformed in key districts we needed to be competitive in."

TWEET

The campaign's general counsel, Dana Remus, issued a letter to Iowa Democratic Party officials on Monday calling for "full explanations and relevant information regarding the methods of quality control you are employing, and an opportunity to respond, before any official results are released."

A strong showing for any of the candidates in Iowa could provide a boost as they turn their attention to New Hampshire, which hosts its primary on Feb. 11.

A weak showing could be particularly damaging to Biden, who is seen as the race's front-runner and leads in national polls. Biden's edge over Sanders in national polling has declined in recent weeks.

CNBC's Yelena Dzhanova contributed to this report.