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Donald J. Trump is handily leading the field in New Hampshire in the Republican presidential race, according to a new Monmouth University poll, running far ahead of his closest competitors, Senator Ted Cruz of Texas and Gov. John Kasich of Ohio.

The results — showing Mr. Trump 18 percentage points ahead of Mr. Cruz and Mr. Kasich — dovetail with other surveys released in recent days from Fox News and NBC/Wall Street Journal/Marist, which also showed Mr. Trump with a strong lead in the state. Those surveys showed different candidates for the second-, third- and fourth-place positions in the race, pointing to the fluidity of the field.

In the Monmouth survey, Mr. Trump is at 32 percent among likely Republican voters. He is followed by Mr. Kasich and Mr. Cruz at 14 percent. Senator Marco Rubio of Florida had the backing of 12 percent, Gov. Chris Christie of New Jersey was at 8 percent, Carly Fiorina had 5 percent, and former Gov. Jeb Bush of Florida and Senator Rand Paul of Kentucky were tied at 4 percent. Ben Carson, at 3 percent, has seen his support crater.

About 32 percent of voters say they’ve already made up their mind, and Mr. Trump’s supporters are the most committed, with 46 percent saying they will definitely vote for him. What’s more, Mr. Cruz remains the strong second preference of many voters, with about 21 percent saying he would be their second choice. The next closest is Mr. Christie, with 12 percent.

The most important issue for the voters was national security and terrorism, with the economy and jobs coming in a distant second place.

The survey of 414 likely Republican primary voters was taken by phone from Thursday through Sunday, and has a margin of sampling error of plus or minus five.percentage points.

The primary will fall on Feb. 9. Mr. Trump, in an interview with NBC’s “Meet the Press” on Sunday, made clear he has no plans to exit the race despite persistent speculation from pundits that he will drop out if he fares poorly in Iowa, where Mr. Cruz leads in many polls. To some extent, the change in expectations — that Iowa is Mr. Cruz’s to lose — has helped Mr. Trump with three weeks until the caucuses take place.