MSNBC's Andrea Mitchell asked Graham whether the real estate mogul should apologize for letting a voter's claim that Obama was Muslim go unchallenged at a Thursday campaign stop.
"Yes. He should come on television. Say 'I made a mistake,'" Graham said. "We all make mistakes. He's new to this business."
Graham drew a distinction between Trump's hands-off approach to the voter's false statement and the way his ally Sen. John McCain (R-AZ) handled a similar situation during the 2008 presidential election. When a woman attending one of McCain's town hall meetings called Obama an "Arab," the then-Republican presidential nominee corrected her and called him a "decent family man."
"This happens to all of us. It happened to John McCain," Graham told Mitchell. "You gotta push back. We are trying to be the leader of a nation here."
A significant percentage of Trump supporters do believe that the President actually is a Muslim—two-thirds, according to a recent survey from Democratic-leaning Public Policy Polling—and Graham suggested that Trump's well-known "birther" streak contributed to that perception among his supporters.
"Mr. Trump in many ways is responsible for this, by creating this idea that maybe Obama was born in Kenya, not Hawaii," he said. "Saying that most illegal immigrants are rapists and drug dealers. He's playing into this hateful narrative. It's now time for him to set it right."