Stewart introduced Clinton by saying, "She's here solely for one reason: to publicly and definitively declare her candidacy for president of the United States."
That proved not to be true.
The two moved on to just about every issue in national and international politics that Clinton faced as secretary of state, including the violence and tension between Israel and the Palestinians.
"We're really in a terrible dilemma," she said, noting there was an offer of a cease-fire brokered by Egypt that Israel accepted but Hamas rejected.
She said that "their identity comes from being the violent resistance."
Stewart also plugged Clinton's new book, "Hard Choices", holding it up to the camera, calling it an "eyewitness view to the history of those four years."
But he kept returning to everyone's main question: the 2016 presidential race, saying, "I think I speak for everybody when I say, no one cares (about the book), they just want to know if you're running for president."
Clinton's book is No. 2 on The New York Times' nonfiction best-seller list. The hardcover is right behind the No. 1 best-seller, Edward Klein's "Blood Feud," which details the alleged animosity between the Clinton and Obama families.
Clinton last appeared on "The Daily Show" during her 2008 presidential campaign.
The show will air later Tuesday.