Radio host Paul Gambaccini says Chris Moyles should be sacked after he made a joke which mentioned Auschwitz.
The outspoken Radio 1 presenter was speaking on his morning show about appearing on BBC1's Who Do You Think You Are?, in which celebrities learn about their genealogy.
"Unlike a lot of The Who Do You Think You Are? shows I didn't go to Auschwitz," he said.
"Pretty much everyone goes there whether or not they're Jewish. They just seem to pass through there on their way to Florida."
The BBC apologised for Moyles' "misjudged" comments but Radio 2 presenter Gambaccini believes the breakfast programme DJ should be dismissed.
"I find his continual presence on Radio 1 unacceptable. Chris Moyles should be gone," Gambaccini said in a lecture at Oxford University.
"His recent comments about Auschwitz involved real people and their ancestors. That is no joking matter for them.
"To encourage this or sit by whilst it happens is unprofessional. He has done it so many times. He has no sense of responsibility."
Gambaccini, who hosts a Saturday evening show on Radio 2, was speaking in his final lecture as the university's News International visiting professor of broadcast media.
He also criticised Moyles for allegedly homophobic remarks to singer Will Young, a close friend of the DJ.
"I am nauseated by the Radio 1 press office constantly rationalising his behaviour," Gambaccini added.
"If we do not get our own house in order, then sooner or later somebody else will and they might break the furniture in the process."