Cruz's win was a breakthrough for Republican Party forces battling to block the controversial New York billionaire, and it raised the prospect of a prolonged nominating fight that could last to the July convention.
Democratic presidential contender Bernie Sanders also won in Wisconsin, gaining momentum in his fight against front-runner Hillary Clinton and trimming her commanding lead in delegates.
Trump had 737 convention delegates to Cruz's 481 heading into the vote, leaving him 500 delegates short of the 1,237 needed to win the nomination. Cruz and Ohio Governor John Kasich, the other remaining Republican contender, hope to stop Trump short of a first-ballot victory and trigger a contested convention.
Cruz, a conservative U.S. senator from Texas, was aided in Wisconsin by the backing of Republican Governor Scott Walker, who had dropped his own presidential bid in September. Party establishment figures, worried that Trump will lead Republicans to a broad defeat in November, have banded together to try to stop him.
The Wisconsin primary followed a difficult week for Trump, who was forced to backtrack after saying women who have abortions should face punishment if the procedure is outlawed, and who voiced support for his campaign manager after he was charged with misdemeanor assault for grabbing a reporter.
In the Democratic race, the win for Sanders, a U.S. senator from Vermont, is his sixth in the last seven presidential nominating contests, but he still faces a difficult task to overtake Clinton as the presidential nominating race moves to New York on April 19 and to five other Eastern states on April 26.
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