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Donald J. Trump‘s popularity continues to rise nationally, according to a new Quinnipiac University poll that shows him with more than double the support of his closest Republican contender.

The poll found that 39 percent of Republicans across the country support Mr. Trump, while 19 percent back Senator Marco Rubio of Florida and 18 percent back Senator Ted Cruz of Texas.

Gov. John R. Kasich of Ohio, Jeb Bush and Ben Carson sit in the mid-single digits and make up the bottom tier of the Republican field.

The poll showed Mr. Trump with his highest level of national support to date among Republicans. Although Mr. Trump is viewed as being the most electable and the best leader in the field, Mr. Rubio beats him when it comes to empathy, honesty and shared values.

Things are tighter for the Democrats, where Hillary Clinton leads Senator Bernie Sanders of Vermont by 44 percent to 42 percent. As with the Republicans, Mrs. Clinton wins on electability and leadership, but Mr. Sanders is seen as more truthful and better at relating to the needs of voters.

The Quinnipiac survey had a margin of error of plus or minus four percentage points.