Republican Senator Ted Cruz beat billionaire Donald Trump in Iowa on Monday while Democrats Hillary Clinton and Bernie Sanders remained deadlocked in the first presidential nominating contests of the 2016 White House race.

Cruz, a conservative lawmaker from Texas, won with 28 percent of the vote compared to 24 percent for businessman Trump in the Republican contest. Marco Rubio, a U.S. senator from Florida, came in third with 23 percent, easily making him the leader among establishment Republican candidates.

Clinton, a former secretary of state, and Sanders, a self-described democratic socialist U.S. senator from Vermont, both came in at roughly 50 percent with 95 percent of the state's precincts reporting results. Sanders declared the results a tie.

Former Maryland Governor Martin O'Malley, who had trouble gaining any traction in the Democratic race, suspended his campaign. He took third place with less than one percent.

Cruz's win and Rubio's strong showing could dent the momentum for Trump, whose candidacy has alarmed the Republican establishment and been marked by controversies such as his calls for a temporary ban on Muslims entering the United States.

"Tonight is a victory for courageous conservatives across Iowa and all across this great nation," Cruz, 45, said during a victory speech that lasted more than 30 minutes. Buoyed by evangelical voters, Cruz thanked God. He said the results showed that the nominee would not be chosen by the media, the Washington establishment or lobbyists.

Trump, 69, congratulated Cruz and said he still expected to win the Republican nomination for the Nov. 8 election.

"I'm just honoured, I'm really honoured," Trump told supporters. He said he looked forward to the next contest next week in New Hampshire, where polls show him ahead.

Clinton, 68, said she was breathing a "big sigh of relief" after the results. She lost to then-Senator Barack Obama in 2008. The former first lady congratulated Sanders and did not declare victory in her remarks.

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"It is rare that we have the opportunity we do now to have a real contest of ideas,” she said.

Sanders, 74, said he and Clinton were in a "virtual tie" and said he was overwhelmed.

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