GOP presidential front-runner Donald TrumpDonald TrumpMuhammad Ali Jr. detained by immigration at Florida airport Two progressive activists were behind Trump Russian flag prank at CPAC Tom Perez embodies the Democratic Party. This is why he should lead it. MORE enjoys a comfortable leads in the early-voting states of New Hampshire and South Carolina, according to a CBS News Battleground Tracker poll released Sunday morning that also shows Ted CruzTed CruzBrietbart CEO reveals that Trump donors are part owners At CPAC, Trump lashes out at media Conquering Trump returns to conservative summit MORE holding the top spot in Iowa.

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Trump has 32 percent support in New Hampshire, followed by Cruz, with 14 percent, Marco Rubio, with 13 percent and New Jersey Gov. Chris Christie, with 11 percent. 

Christie had just 5 percent support in the Granite State last month, CBS noted.

Trump also holds a 15-point lead over Cruz in South Carolina, according to the poll.

Cruz holds a 9-point lead over Trump in Iowa, 40 percent to 31 percent, pollsters found. Rubio lands in third place, with 12 percent. Evangelicals have boosted Cruz, the network said, as have former backers of Ben Carson, who has slipped to fourth place in Iowa, with 6 percent.

Cruz easily tops Trump among respondents in Iowa who say “faith and religion” matters more than terrorism and the economy, CBS added. 

Among the Democratic presidential field, front-runner Hillary Clinton maintains her hold on the top spot by 5 points in Iowa and 36 points in South Carolina; Bernie Sanders leads by 14 points in New Hampshire.

YouGov, an online polling firm, conducted a total of 3,812 interviews between Dec. 13 and 17. The results have a 5.7 percentage point margin of error in New Hampshire, a 5.3-point margin in Iowa and a 5-point margin in South Carolina.

Updated at 3:19 p.m.