Iowa's Democratic Party said early Tuesday that former Secretary of State Hillary Clinton had gained an insurmountable lead over Vermont Sen. Bernie Sanders in the state's caucuses, but stopped short of officially declaring her the winner — while Texas Sen. Ted Cruz scored a decisive win over Donald Trump in the Republican caucuses, with Florida Sen. Marco Rubio a close third. 

Early Tuesday, the Iowa Democratic Party said Clinton had been awarded 699.57 state delegate equivalents while Sanders had received 695.49 state delegate equivalents with one precinct outstanding. That precinct was worth 2.28 state delegate equivalents — not enough for Sanders to make up the deficit.

The Clinton campaign quickly issued a statement declaring victory, saying, "Statistically, there is no outstanding information that could change the results and no way that Senator Sanders can overcome Secretary Clinton's advantage." However, a number of news outlets, including Fox News, did not immediately call the contest for the former secretary of state. 

In at least three precincts, the Democratic outcome was so close that party officials ordered a coin toss to determine which candidate should receive an extra county convention delegate, a longstanding tiebreaking method. The Des Moines Register reported that Clinton won all three coin flips at precincts in Des Moines, Davenport, and Ames.

Despite his apparent defeat, the result reflected a strong showing for Sanders, who had trailed Clinton by nearly 30 points over the summer. Sanders said the results sent a “profound message” to the media and political establishment.

Cruz, too, cast his victory as a message to the Republican establishment.

“Tonight is a victory for the grassroots. Tonight is a victory for courageous conservatives across Iowa and all across this great nation,” Cruz told cheering supporters.

Speaking to supporters at Drake University, Clinton said she was "breathing a big sigh of relief" about the outcome.

"Thank you Iowa. I want you to know that I’ll keep standing up for you, keep fighting for you. Join me. Let’s go win that nomination,” she said.

Sanders noted that Iowa's 44 Democratic national convention delegates would be distributed almost evenly between the two candidates. The Associated Press reported that Clinton had captured at least 22 delegates to Sanders' 21, with the remaining one going to the statewide winner. 

Sanders touched on familiar themes during his speech, saying his campaign was about the people and “not billionaires buying elections.”

En route to New Hampshire, where he holds a substantial lead in the polls ahead of the Feb. 9 primary, Sanders vowed, "We're in this to the convention, and I think this [result] shows the American people we're a campaign that can win.‎"

In the Republican campaign, Cruz fought hard in recent weeks to make up lost ground in the polls and was helped in part by a sophisticated ground operation. He also hammered Trump for his decision to skip last week's Republican debate. 

Meanwhile, Rubio's stronger-than-expected third place finish was helped in large part by late deciders. Entrance polling conducted by Fox News found that 35 percent of GOP caucus-goers made their choice within the last few days of the race. Of those, 30 percent broke for Rubio.

Rubio's campaign also suggested Trump’s debate boycott helped change the dynamic in the race.

With all but one precinct reporting, Cruz had 28 percent, Trump had 24 percent and Rubio had 23 percent. Retired neurosurgeon Ben Carson placed a distant fourth in the race with 9 percent, while Kentucky Sen. Rand Paul placed fifth with 5 percent.

An energized Rubio touted the results at a post-caucus rally.  

“For months they told us we had no chance. … They told me I needed to wait my turn,” Rubio said. “But tonight … here in Iowa, the people in this great state sent a very clear message. After seven years of Barack Obama, we are not waiting any longer to take our country back.” 

Trump, for his part, argued he beat initial expectations by placing second and predicted he'd still win in New Hampshire next week. 

“We will go on to get the Republican nomination, and we will go on to easily beat Hillary or Bernie or whoever the hell they throw up there,” he said. He closed his speech by saying: "I think I might come here and buy a farm, I love it.”

Republicans voted by private ballot. The state's 30 Republican delegates are awarded proportionally based on the vote, with at least eight delegates going to Cruz, seven to Trump and six to Rubio.

Two candidates dropped their presidential bids after poor showings. Former Maryland Gov. Martin O'Malley, who was pulling in about 1 percent support, suspended his campaign  for the Democratic nomination Monday night. And on the GOP side, former Arkansas Gov. Mike Huckabee also suspended his campaign. 

Interest and turnout were high on both sides. Republican officials said there were more than 180,000 people at Monday's GOP caucuses, up from the previous high of about 121,000 in 2012. The Iowa Democratic Party said their caucuses drew 171,109 supporters, well short of the record 240,000 caucus-goers in 2008.

Several caucus sites remained open longer to accommodate long lines; some even ran out of registration forms or ballots.

Cruz rose from the middle of the Republican pack last year to overtake Trump on Monday. His victory disrupts Trump's front-runner narrative and could jolt the GOP race, where candidates have struggled for months to arrest Trump’s rise. 

According to entrance polling of Republican caucus-goers conducted by Fox News, Cruz won by garnering the support of evangelical Christians and those who wanted a candidate who shares their values. Evangelical Christians made up 62 percent of Republican caucus-goers — up from 56 percent in 2012 — and of those, 33 percent backed the Texas senator. 

On the Democratic side, Sanders overwhelmed Clinton among caucus-goers under 30, a group that he won 84 percent to 14 percent. However, that constituency only made up 18 percent of all Democratic caucus-goers. 

On the other hand, 55 percent of all Democratic caucus-goers said they wanted the next president to continue President Obama's policies. Clinton won the support of 68 percent of that constituency.

The Iowa caucuses have had a mixed record in recent cycles, particularly on the Republican side, in picking the eventual nominees. 

The GOP caucus winners in 2008 and 2012 were Huckabee and former Pennsylvania Sen. Rick Santorum, respectively, neither of whom won the nomination.

Eight years ago, though, Obama’s Iowa win helped set him on the trajectory to claim first the Democratic nomination, then the presidency.

Fox News’ Ed Henry and Jake Gibson and The Associated Press contributed to this report.