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Donald J. Trump’s Republican rivals will be playing catch-up ahead of the New York primary, according to a new poll released on Wednesday that shows the Manhattan businessman holding a substantial lead in his home state.

A survey from Monmouth University found that 52 percent of likely Republican primary voters support Mr. Trump. Gov. John Kasich, who has only won his state of Ohio, comes in second with 25 percent, and Senator Ted Cruz of Texas trails with 17 percent.

Mr. Trump is showing particular strength in New York City, Long Island and western New York. If the numbers hold up, Mr. Trump could net most of the state’s 95 delegates on April 19.

Although Mr. Trump has been criticized in recent weeks for his comments on abortion and nuclear weapons policy, most New York Republicans were unfazed by the controversies, the poll suggested.

Like many national polls, Monmouth’s survey also shows Mr. Kasich as the strongest candidate in a hypothetical general election contest against Hillary Clinton. However, none of the Republicans are likely to turn New York red in November.

“It is interesting that Kasich would be a stronger nominee in Trump’s home state, but it is purely academic,” said Patrick Murray, director of Monmouth University’s poll. “There is almost no probability that any Republican would be able to win New York’s electoral votes.”