Cruz's gains in the polling mark the first time since November that one of Trump's rivals has threatened his lead in support among Republicans in the race to be party nominee for the Nov. 8 election.
The gains coincided with a bumpy patch for Trump, who was forced to backtrack last week after saying women who had 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 allegedly grabbing a reporter.
Cruz, a senator from Texas, got 35.2 per cent of support to Trump's 39.5 per cent, the poll of 568 Republicans taken April 1-5 found.
The numbers put the two within the poll's 4.8 percentage-point credibility interval, a measure of accuracy.
Cruz and Trump were also briefly about even early last week.
But as recently as a month ago, when Senator Marco Rubio was also still a candidate, Cruz trailed Trump in the Reuters/Ipsos polling by about 20 points.
Ohio Governor John Kasich, the only other candidate left in the race for the Republican Party nomination, placed third in the April 1-5 poll with 18.7 per cent.
Trump's support has faltered among women in particular in recent weeks. More than 70 percent of likely women voters said they had an "unfavorable" opinion of Trump, according to the rolling poll average for the five-day period ended April 5.
In the Democratic race, front-runner Hillary Clinton held a nationwide lead in the poll of about 7 points over US Senator Bernie Sanders of Vermont.
Cruz and Sanders easily won their Wisconsin presidential primary contests on Tuesday night. Sanders would still face a difficult task overtaking Clinton as the nominating contest, but Cruz's double-digit win over Trump was seen as a breakthrough for Republican Party forces battling to block him.
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