London Mayor Boris Johnson clashed with Asim Qureshi, the research director of the advocacy group Cage during a live LBC radio show, over the group's portrayal of cold-blooded Islamic State (Isis) killer Jihadi John as a victim.
Cage has been heavily criticised for suggesting the British secret services played a role in radicalising Mohammed Emwazi, the notorious executor of Isis captives.
Johnson told Qureshi: "I watched you explain how he had been seeking 'a career overseas' and had been impeded by the security services in finding his vocation. Actually, he was going off to join a terrorist group in Somalia.
"I really, really think that the focus of your indignation and your outrage should be on people who go out to join groups that throw gays off cliffs, that behead people who don't subscribe to their version of Islam, that glorify in the execution of innocent journalists and aid workers. They should be the object of your wrath, not the security services who are trying to keep us safe."
Details have emerged about Emwazi's life before he became one of the world's most famous terrorists. He was reportedly bullied at school, but went on to be a "model employee" at a company in Kuwait.
Meanwhile, Amnesty International is considering whether to cut ties with Cage for its apparent failure to sufficiently condemn Emwazi.