If an announcement of a presidential candidacy were as rocky as Comedy Central’s introduction of Trevor Noah, “The Daily Show” would have a field day with it.

Since Mr. Noah, a 31-year-old South African comic, was named to succeed Jon Stewart as that show’s host, he has been embroiled in a controversy over jokes he posted on Twitter about women and Jews that some viewed as offensive and others as merely lame. (He was the subject of a brief defense by Mr. Stewart.)

Now there’s a new dust-up: Russell Peters, a popular and well-traveled Canadian stand-up comic, called Mr. Noah “a thief” in a television interview in Singapore. “He’s stolen material from David Kau,” he said, referring to another South African comic. “He’s stolen material from myself.”

Mr. Peters did not provide specifics, and he backtracked on Twitter on Wednesday, referring to his comment as a “prank.”