The debunked conspiracy theory among conservative activists dubbed "birthers" charges that Obama is not constitutionally qualified to serve in the White House. Romney has said he believes Obama was born in America, but he has not condemned Trump's comments.
Democrats contend it's the latest example of Romney's reluctance to confront the more extreme elements in his party.
"A lot of people do not think it was an authentic certificate," Trump told CNN of Obama's birth certificate, just hours before he was set to host Romney's finance event at the Trump International Hotel in Las Vegas.
Such allegations have been repeatedly proven false. The state of Hawaii recently re-affirmed that Obama was born there.
Trump's comments, repeated in several media interviews Tuesday, overshadowed Romney's visit to Nevada, one of a handful of swing states expected to decide the presidential contest in November. Trump also upstaged news from Texas that Romney had collected enough delegates to clinch the Republican presidential nomination.
Romney did not address the issue directly at separate events in Colorado and Nevada, but on Monday night he told reporters aboard his campaign plane that Trump is entitled to his opinion. Even as Trump-related criticism from Democrats and Republicans intensified in recent days, Romney showed no sign of distancing himself from the polarizing figure.
"I don't agree with all the people who support me. And my guess is they don't all agree with everything I believe in," Romney said. "But I need to get 50.1 percent or more. And I'm appreciative to have the help of a lot of good people."
Trump remains popular among the conservative base and boasts ties to deep-pocketed donors. The Las Vegas event was expected to raise $2 million, but Romney's ties to Trump extend beyond that single fundraiser. He has recorded automated phone calls for Romney, hosted a fundraiser for his wife, Ann, in New York, and pressed the candidate's case as a television surrogate.
When Romney's campaign plan arrived at the Las Vegas airport Tuesday, it parked within sight of Trump's plane - the businessman's name emblazoned on the side in large gold letters.
Former House Speaker Newt Gingrich, once a rival for the GOP nomination and now a Romney supporter, suggested that the Trump issue will not derail Romney's campaign.
"Gov. Romney's not distracted. The Republican Party's not distracted," said Gingrich, who attended the Trump fundraiser. "We believe that this is an American-born job-killing president. Other people may believe that he was born somewhere else and still kills jobs."
The Obama campaign released a video Tuesday criticizing what it considers Romney's unwillingness to stand up to Trump and the more extreme elements in his party. There have been other examples in recent weeks that underscore Romney's delicate push to win over skeptical conservatives while appealing to moderates and independents who generally deliver general election victories.
"Mitt Romney's continued embrace of Donald Trump and refusal to condemn his disgraceful conspiracy theories demonstrates his complete lack of moral leadership," Obama's deputy campaign manager, Stephanie Cutter, said in a statement. "If Mitt Romney lacks the backbone to stand up to a charlatan like Donald Trump because he's so concerned about lining his campaign's pockets, what does that say about the kind of president he would be?"
While Trump asserts that the matter of Obama's birth is a "good issue" for Romney, conservative commentator George Will questioned the "cost benefit" of Romney appearing with Trump.
"The cost of appearing with this bloviating ignoramus is obvious, it seems to me," Will said Sunday. "Donald Trump is redundant evidence that if your net worth is high enough, your IQ can be very low and you can still intrude into American politics. ... Again, I don't understand the benefit. What is Romney seeking?"
Trump revived the false claims about Obama's birthplace late last week, citing a story about a literary agency that mistakenly listed that Obama was born in Kenya.
While Romney briefly addressed the issue Monday, senior aide Eric Fehrnstrom declined to condemn Trump's remarks in a recent interview.
"I can't speak for Donald Trump ... but I can tell you that Mitt Romney accepts that President Obama was born in the United States," Fehrnstrom said. "He doesn't view the place of his birth as an issue in this campaign."