Sen. Ted Cruz is closing the gap against Donald Trump, though Trump still holds a comfortable lead over the rest of the pack, according to a new Fox News poll.

The survey has Trump at 35 percent nationally and Cruz at 20 percent, a narrower lead for the businessman than in a mid-December poll in which Trump was at 39 percent and Cruz was at 18 percent.

As Cruz emerges as the frontronner to win the first nominating contest in Iowa and gains nationally, Trump has been raising questions about Cruz's eligibility to be president given that he was born in Canada, even though the consensus among legal scholars is that Cruz is eligible because his mother was a U.S. citizen.

Trailing Trump and Cruz in the latest poll are Rubio at 13 percent and Ben Carson at 10 percent. No other candidate polls higher than 4 percent.

National polls are typically less reliable than early state polls in predicting the ultimate nominee, because there is no national primary and the results of early contests tend to change the national polling. In other Fox polls released on Friday, Trump was ahead in New Hampshire and Cruz was ahead in Iowa.

Fox News Poll

2016 GOP Nominee Preference

Among Republican Primary Voters

Now Dec. 16-17

Trump 35% 39%

Cruz 20% 18%

Rubio 13% 11%

Carson 10% 9%

Bush 4% 3%

Fiorina 3% 3%

Christie 2% 3%

Kasich 2% 2%

Paul 2% 3%

Huckabee 1% 1%

January 4-7, 2016

Republican Primary Voters ± 4.5% Pts.