On Tuesday, during what will be his final appearance opposite Stewart on the show, the president issued a tongue-in-cheek executive order requiring Stewart to stay in his position as host.
"I can't believe you're leaving before me," Obama told Stewart, whose final show is August 6. "In fact, I'm issuing a new executive order that Jon Stewart cannot leave the show."
During the chat, Stewart couldn't resist bringing up his favorite subject of late: the antics of Republican presidential candidate Donald Trump.
"I'm sure the Republicans are enjoying Mr. Trump's dominance of their primary," Obama quipped.
The interview touched on serious topics too, including ISIS, the recent nuclear deal with Iran, and Obama's goals for his remaining year and a half in office. There's "a bunch of other things we want to get done" in that time, Obama promised, including climate change legislation.
Watch the full episode of The Daily Show below, and see President Obama's extended interview - with portions that didn't make the broadcast version - here.