Donald Trump
Republican presidential candidate Donald Trump speaks at the Iowa Faith & Freedom Coalition's 15th annual Family Banquet and Presidential Forum in Des Moines, Sept. 19, 2015. Steve Pope/Getty Images

Republican presidential candidate Donald Trump said there is a “very severe problem” with some Muslims when he spoke with “Meet the Press” Sunday, but he declined to comment on whether or not he would support a Muslim for the presidency of the U.S.

“We can be politically correct and say there is no problem whatsoever, but the fact is, there is a problem with some, and it's a very severe problem, and it's a problem that's taking place all over the world,” he said.

In the same breath, Trump told “Meet the Press” host Chuck Todd: “Muslims are excellent. I know so many Muslims that are such fabulous people.”

When asked specifically if he would support a Muslim as president of the U.S., Trump said he would not currently address the issue, adding: “Some people have said it already happened.”

That remark followed a controversy that erupted last week when Trump was asked a question by an audience member at a New Hampshire town hall meeting. The man said President Barack Obama is a Muslim who was not born in the U.S. While Trump has said he does not need to defend the president from such accusations, Trump himself has fueled speculation that Obama was born outside of the U.S. In 2011 he held a press conference and called on Obama to release his birth certificate.

Trump said Sunday that he accepted Obama’s word that he is a Christian, but when asked about Obama’s citizenship, Trump responded, “I just don't want to discuss it.”

Republican presidential candidate Ben Carson also spoke with “Meet the Press” Sunday. Carson said he would not support a Muslim as president of the U.S. “I would not advocate that we put a Muslim in charge of this nation,” he said. “I absolutely would not agree with that.”

Trump has elicited a love-hate response from participants in Iowa polls. While Trump was leading all GOP presidential candidates in support, he also led the pack in terms of candidates people would not support.