Cruz, a conservative lawmaker from Texas, won with 28 per cent of the vote compared to 24 per cent for businessman Trump, according to MSNBC.
Marco Rubio, a U.S. senator from Florida, came in third place with 23 per cent, making him easily the leader among establishment candidates.
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Former Maryland Governor Martin O'Malley, who had trouble gaining any traction in the Democratic race, planned to suspend his campaign at 9:30 p.m. CST, according to a Democrat with knowledge of his plans.
Sanders, Clinton deadlocked
Among Democrats, Hillary Clinton and Bernie Sanders were deadlocked in a tight race. Vote counts at the 90 per cent point in tabulations showed Clinton and Sanders in a virtual tie.
Clinton, the former secretary of state, U.S. senator and first lady, had been expected to cruise to victory in Iowa and beyond. But Sanders has appealed to the Democrats’ liberal base, especially the young, who are concerned about growing income inequality and the shrinking of the middle class.
Huckabee, O'Malley suspend campaigns
Former Arkansas Governor Mike Huckabee said he was suspending his campaign for the Republican party nomination, while Former Maryland Governor Martin O’Malley ended his longshot bid for the Democratic nomination
"I am officially suspending my campaign," Huckabee said on Twitter. "Thank you for all your loyal support."