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Donald J. Trump is heading into 2016 with a commanding lead atop the field of Republican presidential candidates, according to a new national CNN/ORC poll that shows him widening his advantage about six weeks ahead of the Iowa caucuses.

The survey, released on Wednesday, found that 39 percent of Republican voters back Mr. Trump for the nomination while 18 percent support Senator Ted Cruz and 10 percent are behind Senator Marco Rubio of Florida and Ben Carson. The billionaire developer has extended his lead from a month ago and essentially now has more support than his three top challengers combined.

The poll represents good news for Mr. Trump, who has seen Mr. Cruz gain ground on him in Iowa and nationally, as evangelical Christians have found the Texas senator to be increasingly attractive.

But those queried by CNN/ORC (the Opinion Research Corporation) found that Mr. Trump is still viewed as the strongest Republican to handle the economy, immigration and terrorism. His popularity has endured despite provocative proposals such as a temporary ban on Muslim immigration.

The rest of the Republican field remains muddled as 2015 draws to a close. Former Gov. Jeb Bush of Florida, Gov. John Kasich of Ohio and Gov. Chris Christie of New Jersey are banking on strong performances in New Hampshire’s primary on Feb. 9, after the Iowa caucuses on Feb. 1. All three are languishing in the single digits nationally.

The CNN/ORC poll had a margin of error of plus or minus five percentage points.