During an appearance on New Zealand radio station The Rock
on Wednesday, Key played along with a request from the radio hosts to get inside a cage in the studio.
Once in the cage, host Tom Furniss dropped a bar of soap and asked Key to pick it up, as those present howled in laughter.
Key complied, and Furniss told him: "You've got a pretty little mouth, Prime Minister."
"Dropping the soap" is a reference to prison rape. And Furniss' line references one in the film "Deliverance," in which a man is raped by two other men.
'This makes me feel ill'
Key's participation in the stunt drew criticism, with concerns that it made light of sexual violence.
"This makes me feel ill. When the PM thinks it's okay to participate in rape jokes, how can women feel safe?" tweeted Deborah Russell, a feminist commentator and Massey University lecturer.
"The PM playing along with rape jokes makes it very clear how little regard he has for changing the law around sexual violence."
Political commentator Matthew Hooton drew a comparison to another recent radio appearance in which Key tunelessly sang a karaoke version of Mariah Carey's "All I Want for Christmas Is You,"
saying that while the singing had been "goofing around," the cage stunt was "a complete disgrace."
Petition against Key
Auckland psychotherapist Kyle MacDonald started an online petition to have Key stripped of his ambassador role
with White Ribbon over the comments. The petition has received more than 3,000 signatures.
White Ribbon is a global campaign by men who condemn violence against women.
"I have become increasingly concerned about the actions of our Prime Minister, and how they show a complete lack of understanding about the impacts of sexual and physical violence in this country," wrote MacDonald in launching the petition. "His 'prison rape' joke on radio yesterday was the last straw."
Key has not responded to the criticism.
Rape in the spotlight
Rape has been a hot-button political issue in New Zealand recently after a group of female MPs revealed in parliament last month that they had been victims of sexual assault -- then were ordered to leave when the parliament speaker ruled their statements out of order.
The women were speaking out after Key yelled at opposition lawmakers "you back the rapists" during a debate about Australia's treatment of New Zealand criminals being held in detention. Key apologized for the comments earlier this month.
Key's approachable, down-to-earth public persona has proven a political asset for the popular three-term Prime Minister, but he has increasingly raised eyebrows for media appearances that paint him in an unstatesmanlike light.
During an appearance on New Zealand radio station Radio Hauraki in October
, Key answered a series of questions from the hosts about urinating in the shower, masturbation and his pubic hair, among other topics.
When Key sang the Mariah Carey song on air this week, he was opting to do so over the other option the radio hosts had presented him with: pulling a line-up of women's ponytails.
That was a reference to a scandal Key found himself in earlier this year, when a waitress at his local cafe complained he regularly pulled her ponytail
when he visited the eatery.
Key, who said he had apologized to the woman when it was pointed out his actions were unwelcome, was roundly criticized.