Bernie Sanders. REUTERS/Rick Wilking

Hillary Clinton slightly edged out Bernie Sanders to win the Iowa caucuses, according to a statement from the Iowa Democratic Party early Tuesday morning.

The final results were "the closest in Iowa Democratic caucus history," the IDP statement said.

Neither Clinton nor Sanders declared victory in Iowa on Monday night, but both hailed their caucus performances as successes.

Both the former secretary of state and the US senator from Vermont delivered fiery speeches as results continued to show them in a dead heat.

By 11:30 p.m. CT, Clinton had 49.8% of the vote and Sanders had 49.6%, according to the IDP.

During her speech, Clinton said she was "breathing a big sigh of relief," and she shouted, "Thank you Iowa!" as she addressed a crowd of supporters about an hour earlier.

Sanders spoke afterward and said that "while the results are still not complete," it looked like a "virtual tie."

"What Iowa has begun tonight is a political revolution," he said.

The Democratic race plunged into further chaos early Tuesday morning, when the Sanders campaign told reporters, according to multiple reports, that the Iowa Democratic Party informed both campaigns that results from about 90 of the state's more than 1,600 precincts were "missing."

Both candidates addressed their opponent during their speeches.

"I want to take this opportunity to congratulate Secretary Clinton and her organization for waging a very vigorous campaign," Sanders said.

He opened his speech on a victorious note, to thunderous applause and loud cheers, that remembered the large deficit at which he began the race.

"Nine months ago, we came to this beautiful state, we had no political organization. We had no money. We had no name recognition, and we were taking on the most powerful political organization in the United States of America," he said, in a reference to Clinton.

Throughout his remarks, he blasted "billionaires" who "buy elections" and noted that small donations had propelled his campaign.

"I am overwhelmed and I am moved by the fact that millions of people throughout this country have helped volunteer on our campaign, that we have received in this campaign 3.5 million individual contributions," Sanders said.

"People who went to BernieSanders.com, and you know what the average contribution was: It was $27!" he thundered.

Hillary Clinton. REUTERS/Adrees Latif

By contrast, Clinton has relied more on larger donations.

"We do not represent the interests of the billionaire class or Wall Street … and I am very proud to tell you that we are the only candidate on the Democratic side without a super PAC," Sanders continued. "And the reason that we have done so well here in Iowa, the reason I believe we are going to do so well in New Hampshire … The reason is the American people are saying no to a rigged economy."

As Sanders was speaking, he was interrupted several times by cheers, and at one point the crowd started shouting his name, drowning out his speech.

Clinton's event was more subdued. But it, too, had a victorious tone, as Clinton fired up the crowd with a passionate speech about the race ahead.

She congratulated her "esteemed friends and opponents" and said she was "excited about really getting into the debate with Sen. Sanders about the best way forward to fight for us and America."

"It is rare that we have the opportunity that we do now," Clinton said. "To have a real contest of ideas. To really think hard about what the Democratic Party stands for and what we want the future of our country to look like if we do our part to build it."

She then called herself a "progressive" who "gets things done for people."

Clinton listed a litany of issues she wanted to tackle as president: universal healthcare coverage, climate change, clean energy, education for disadvantaged children, college affordability, gun control, women's rights, gay rights, and voting rights.

The third Democratic presidential candidate, former Gov. Martin O'Malley of Maryland, dropped out of the race earlier in the evening.

CNN Washington correspondent Jeff Zeleny said on air that Monday night's outcome "ensures that this race is going to go on for months and months."