Trump is referring to a report last week published by Breitbart that showed the president's literary agent erroneously claiming he was born in Kenya as part of a pitch for a book on race he never completed. The president was born in Hawaii, and his literary agent said last week she was mistaken in claiming otherwise.

But Trump, who has never acknowledged the long-form birth certificate issued by the Obama campaign to be authentic, remains skeptical.

“That’s what he told the literary agent,” Trump insisted. “That’s the way life works … He didn’t know he was running for president, so he told the truth. The literary agent wrote down what he said … He said he was born in Kenya and raised in Indonesia … Now they’re saying it was a mistake. Just like his Kenyan grandmother said he was born in Kenya, and she pointed down the road to the hospital, and after people started screaming at her she said, ‘Oh, I mean Hawaii.’ Give me a break.”

The Democratic National Committee quickly pounced on the statement.

“Once again Mitt Romney is failing the moral leadership test,” said DNC press secretary Melanie Roussell. “Instead of rejecting Donald TrumpDonald John TrumpIvanka Trump pens op-ed on kindergartners learning tech Bharara, Yates tamp down expectations Mueller will bring criminal charges Overnight Cybersecurity: Equifax security employee left after breach | Lawmakers float bill to reform warrantless surveillance | Intel leaders keeping collusion probe open MORE’s ‘birther’ conspiracy theories and divisive attacks, he’s endorsing them by campaigning and fundraising with him."

The anecdote underscores the risk for Romney in embracing Trump, who can frequently stray off message. Earlier this year, Trump was highly critical of House Budget Committee Chairman Paul RyanPaul RyanThe Hill Interview: Budget Chair Black sticks around for now Gun proposal picks up GOP support GOP lawmaker Tim Murphy to retire at end of term MORE's (R-Wisc.) proposed budget, despite widespread embrace by Republicans, including Romney.

"I think the worst thing he can do is strongly embrace that budget if he wants to get elected,"Trump told CNBC. "This will be the single worst move in the Republican Party for many years. This is going to be catastrophic."

Trump has also criticized prominent Republican Super PAC American Crossroads for its ad depicting the president as a "super celebrity," calling the campaign misguided.

Late last year, Romney's son, Matt, created a flap on the campaign trail when he joked about the president's birth certificate. Matt Romney later tweeted an apology, calling the comment "dumb."