Donald Trump tells Savannah Guthrie he's "never had a problem with Muslims," and reiterated his belief that it's not his "obligation" to defend President Obama's faith and citizenship.

"Is the president going to defend me because last night during the Emmy awards people said things about me?" the leading Republican presidential hopeful said in an interview on TODAY Monday. "Is the president going to hold a news conference and defend me? I don’t think so."

Trump has been dogged recently by his failure to correct a campaign supporter who incorrectly called President Obama both a Muslim and "not an American" citizen.

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The incident reminded many of Trump’s role in fueling the “birther” movement, when Obama critics questioned whether he was born in the United States and therefore eligible to be president. The president later provided a copy of his Hawaiian birth certificate but it did not quell doubters, including Trump.

About the man at his New Hampshire campaign event last week who also took issue with a national problem "called Muslims," Trump said he assumed the man “was talking about radical Islam.”

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“It’s an amazing problem. It’s a very big problem and I fully understand that Muslims are great people, and I have many friends — they’re great friends. By the way, they’re concerned with radical Islam, too,” he said.

A new CNN/ORC poll shows Trump's ratings, while still ahead of more than a dozen Republican candidates, taking its biggest drop so far in the campaign. It also shows rival Carly Fiorina surging to second, in large part because of her strong performance during Wednesday’s debate, where she repeatedly took on Trump on various topics.

Trump said he's not worried about Fiorina's rocketing poll rating.

"She’s got a good line of pitter patter," he said. Last week's debate marked the first time many heard her speaking, but "she says the same thing over and over and over." He expressed optimism voters will lose interest once they delve into her business background.

"I don’t see how she could possibly win," he said.

Follow TODAY.com writer Eun Kyung Kim on Twitter.