Billionaire businessman Donald J. Trump has a 10-point over his closest 2016 GOP competitor, Sen. Ted Cruz of Texas, in a national poll on the race for the Republican presidential nomination out Tuesday.

Mr. Trump was at 27 percent in the USA Today/Suffolk University poll, followed by Mr. Cruz at 17 percent, Sen. Marco Rubio of Florida at 16 percent, and retired neurosurgeon Ben Carson at 10 percent.

Former Florida Gov. Jeb Bush was at 4 percent, and Sen. Rand Paul of Kentucky, New Jersey Gov. Chris Christie, and Ohio Gov. John Kasich were all at 2 percent apiece.

“The Republican side is beginning to shake out, at least at the national level,” said David Paleologos, director of the Suffolk University Political Research Center in Boston. “Both Senators Cruz and Rubio are vying hard to be the Republican alternative to Trump, but there are 17 percent undecided still, which keeps the door open for one of the single-digit candidates to make a splash in Iowa or New Hampshire and shake the race up further.”

In a sub-sample of Trump supporters, about 68 percent said they would still vote for Mr. Trump if he ran as an independent candidate. Eighteen percent said they would not and 11 percent said they weren’t sure.

Mr. Trump has pledged to support the eventual GOP nominee and forgo an independent run if he doesn’t secure the party’s nomination as long as he feels he’s being treated fairly.

But he did highlight the 68 percent figure on social media Tuesday, along with a link to a USA TODAY story that had the number in the headline.

“A new poll indicates that 68% of my supporters would vote for me if I departed the GOP & ran as an independent,” Mr. Trump said on Twitter and Facebook.

Mr. Trump has been roundly criticized by Democrats and Republicans alike over the last day or so for proposing on Monday to ban Muslims from traveling to the United States in light of the ongoing terror threat. The survey was taken from Dec. 2-6 — before he rolled out the idea.

On the Democratic side, former Secretary of State Hillary Clinton retained her solid grip on the nomination contest, winning 56 percent support to Sen. Bernard Sanders’ 29 percent and former Maryland Gov. Martin O’Malley’s 4 percent.

But accounting for the survey’s margin of error, she was in a statistical dead heat in head-to-head matchups against Mr. Trump, Mr. Cruz, Mr. Rubio and Mr. Carson.

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