Appearing on the popular Comedy Central series this week, the British politician told Stewart he always liked Bush despite the Republican president's declining popularity worldwide, The Times of London reported Saturday.
"Here's something I find always goes down well, particularly back home: I like him," Blair said during Thursday's broadcast.
Ever the comedian, Stewart was quick to retort regarding the leader of his nation.
"I would probably like him too, if he wasn't in charge of me," Stewart told Blair.
Blair, who is set to teach a Yale University course called "Faith and Globalization," also spoke about the public opposition to the war in Iraq.
"None of this is easy, OK," he told Stewart when pressed on the issue.
The Times said Stewart did praise the former prime minister for his open stance on such opposition when compared to critical responses from top U.S. officials.
"You could never run this country buddy, I'll tell you that much," he joked with Blair.
Celebrity Families of 2014 [PHOTOS]