Donald Trump dominated the rest of the Republican field in the first national poll of 2016, and more than half of his supporters say they are strongly committed to voting to him.

The billionaire businessman won the support of 35 percent of the Republican and Republican-leaning registered voters surveyed in the latest NBC News/SurveyMonkey online tracking poll released Tuesday.

Texas Sen. Ted Cruz came in second place with 18 percent, roughly half of Trump's level of support. Cruz was followed by Florida Sen. Marco Rubio at 13 percent, Ben Carson at 9 percent, and former Florida Gov. Jeb Bush at 6 percent. New Jersey Gov. Chris Christie and Carly Fiorina trailed at 4 and 3 percent, respectively, according to the full results of the poll shared first on MSNBC's "Morning Joe" Tuesday.

Just over half of Trump voters, 51 percent, say they are absolutely certain they will vote for him, while about another 33 percent say they are likely to vote for him. By comparison, Cruz and Rubio face more uncertainty when it comes to their voters. Thirty-six percent of Cruz voters said they were committed, while 26 percent of Rubio voters said the same. Both candidates saw 49 percent of voters saying there is a "large chance" they will vote for either Cruz or Rubio.

Trump won the support of 39 percent of men and 29 percent of women, which had him leading both groups. Cruz had 21 percent support of men and 13 percent of women, while Rubio took 13 percent from men and 14 percent from women.

Former Secretary of State Hillary Clinton continues to lead Democrats, and is ahead of Vermont Sen. Bernie Sanders 53 percent to 36 percent. Former Maryland Gov. Martin O'Malley earned 2 percent and 8 percent said they were not sure.

The online poll was conducted Dec. 28-Jan. 3, surveying 3,181 registered voters among a sample of 3,700. The margin of error for 949 registered Republican voters is plus or minus 3.7 percentage points, while among 1,060 Democrats, the margin of error is plus or minus 3.3 percentage points.