Cruz, a conservative lawmaker from Texas, won with 28 percent of the vote compared to 24 percent for businessman Trump, according to MSNBC.
Marco Rubio, a U.S. senator from Florida, came in third place with 23 percent, making him easily the leader among establishment Republican candidates.
Former Secretary of State Hillary Clinton held a slim lead in the
Democratic race over rival Bernie Sanders, a self-described democratic
socialist U.S. senator from Vermont.
On the Republican side, former Arkansas Governor Mike Huckabee said he was suspending his campaign for the Republican party nomination. Huckabee won the Iowa caucus in 2008.