The audience member stood up at the rally last week in Rochester, New Hampshire and said "we have a problem in this country and it's Muslims."
"Well, he said much more than that," Trump said in the interview. "That was part of the statement."
Later in the interview, set to air Sunday, he said "you don't know that he was a bigot."
Trump told Pelley Muslims are "phenomenal people" and "I love the Muslims," "but like everything else you have people where there are problems."
Trump also rejected the notion that he should have defended Obama, who is a Christian and has produced his birth certificate.
"I don't have to defend President Obama," he told Pelley. "He's not gonna defend me."
Trump, who has called Obama's birthplace into question, was condemned on many fronts for not responding to the audience member.
In the wake of the event, his campaign told ABC News he had trouble hearing the question and that the opinions about Muslims were of the one man in the crowd.