Jon Stewart, who turned Comedy Central’s “The Daily Show” into a sharp-edged commentary on current events, delivering the news in layers of silliness and mockery, said on Tuesday that he would step down after more than 16 years as its anchor.

Mr. Stewart, whose contract with Comedy Central ends in September, disclosed his plans during a taping of the program on Tuesday. Saying that “in my heart, I know it is time for someone else” to have the opportunity he had, Mr. Stewart told his audience that he was still working out the details of his departure, which “might be December, might be July.”

“I don’t have any specific plans,” Mr. Stewart said, addressing the camera at the end of his show, at times seeming close to tears. “Got a lot of ideas. I got a lot of things in my head. I’m going to have dinner on a school night with my family, who I have heard from multiple sources are lovely people.”

“I’m not going anywhere tomorrow,” Mr. Stewart added, “but this show doesn’t deserve an even slightly restless host, and neither do you.” Comedy Central did not elaborate on the future of the show, except to say that it “will endure for years to come.”