Donald TrumpDonald John TrumpWSJ: Trump ignored advice to confront Putin over indictments Trump hotel charging Sean Spicer ,000 as book party venue Bernie Sanders: Trump 'so tough' on child separations but not on Putin MORE leads Ted CruzRafael (Ted) Edward CruzWashington needs to end hidden inflation tax on our capital gains GOP tax writer introduces bill to reduce capital gains taxes Senators push to clear backlog in testing rape kits 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 RubioHillicon Valley: Trump's Russia moves demoralize his team | Congress drops effort to block ZTE deal | Rosenstein warns of foreign influence threat | AT&T's latest 5G plans On The Money: Trump 'ready' for tariffs on all 0B in Chinese goods | Trump digs in on Fed criticism | Lawmakers drop plans to challenge Trump ZTE deal Overnight Defense: White House 'not considering' Ukraine referendum | Pompeo hopeful on plans for Putin visit | Measure to block ZTE deal dropped from defense bill 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 walks a tightrope with comments on NATO Progressive politics have done nothing to help black America Is civility in America really dead? 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 PaulThe Hill's Morning Report — Trump and Congress at odds over Russia GOP leader blocks resolution backing intelligence community on Russia Rand Paul blocks Sanders's Russia resolution, calls it 'crazy hatred' against Trump 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.