Donald TrumpDonald John TrumpZuckerberg launches public defense of Facebook as attacks mount Trump leaning toward keeping a couple hundred troops in eastern Syria: report Warren says making Israel aid conditional on settlement building is 'on the table' MORE leads Ted CruzRafael (Ted) Edward CruzHillicon Valley: GOP lawmakers offer election security measure | FTC Dem worries government is 'captured' by Big Tech | Lawmakers condemn Apple over Hong Kong censorship Lawmakers condemn Apple, Activision Blizzard over censorship of Hong Kong protesters The Hill's Morning Report — Trump's impeachment jeopardy deepens MORE by 2 percentage points in a new poll from Iowa, suggesting a tightening presidential race ahead of the state’s Feb. 1 caucuses.

Trump leads the GOP field, with 31 percent support, in Quinnipiac University's new poll, followed closely by Cruz's 29 percent. That slim lead is within the poll’s 4-point margin of error.

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Voters view Cruz more favorably than they view Trump, however, and more are open to the possibility of voting for him, according to the new findings. 

This is only the third poll of the last 11 in Iowa in which Trump is on top, according to aggregation by RealClearPolitics. Other recent polls have shown Cruz in first place.

Trump in the last week has stepped up attacks on Cruz’s birthplace. Cruz was born in Canada, and Trump argues Democrats could make a case that he is not qualified to be president because he is not a natural born citizen.

Cruz was born to an American mother, and his campaign has argued he is qualified to be president just like 2008 GOP presidential nominee John McCain, who was born in the Panama Canal zone. Legal experts have long agreed that the Constitution's natural born citizen requirement includes those born to U.S. citizens outside the country.

In the poll, Cruz won more than one-third of the support of white, evangelical Republicans, an important constituency for him that typically makes up the majority of GOP caucusgoers. Trump attracted 27 percent with that group, and Marco RubioMarco Antonio RubioTurkey says soldier killed despite cease-fire in Syria White House staggers after tumultuous 48 hours Erdoğan got the best of Trump, experts warn MORE received 13 percent, but other candidates won more than one-tenth of the evangelical vote.

Cruz outperformed Trump among people with college educations, with an income between $50,000 and $100,000, and who consider themselves very conservative. On the flip side, Trump did better among those without a college degree, and those making less than $50,000 and more than $100,000.

In the Quinnipiac poll, Rubio sits in third place, with 15 percent support, followed by Ben CarsonBenjamin (Ben) Solomon CarsonTrump officials say aid to Puerto Rico was knowingly stalled after Hurricane Maria Yes, President Trump, we do have a homelessness crisis and you're making it harder for us to address New HUD rule would eliminate housing stability for thousands of students MORE, at 7 percent, and Chris Christie, at 4 percent. Jeb Bush has slipped to 3 percent, tied with Mike Huckabee, who won the caucuses in 2008. John Kasich and Rand PaulRandal (Rand) Howard PaulTurkey sanctions face possible wall in GOP Senate Trump-Graham relationship tested by week of public sparring Overnight Defense — Presented by Boeing — Pence says Turkey agrees to ceasefire | Senators vow to move forward with Turkey sanctions | Mulvaney walks back comments tying Ukraine aid to 2016 probe MORE scored 2 percent; Carly Fiorina and Rick Santorum received 1 percent.

Quinnipiac surveyed 602 likely Republican caucusgoers in Iowa between Jan. 5 and Jan. 10.

Updated at 1:11 p.m.