Conservative frontbencher Alan Duncan may face a police investigation after joking on TV that he wanted to murder Miss California because she disagrees with gay marriage.

Mr Duncan, who became the first Conservative MP to form a same-sex civil partnership last year, was appearing on the BBC’s satirical news quiz, Have I Got News For You.

Watch Alan Duncan’s comments

He made the joke as panelists discussed Carrie Prejean, the Miss USA contestant who lost out on the title after stating her belief that marriage should be between a man and a woman.

Mr Duncan said: “If you read that Miss California has been murdered, you will know it was me, won’t you?”

Fellow panelist Katy Brand was visibly shocked that Mr Duncan had made the statement on television, while Ian Hislop, editor of Private Eye magazine, remarked: “Nothing like freedom of speech from a Tory, eh? She disapproves of same-sex marriage so she deserves to die by your hand!”

Mr Duncan’s joke has prompted complaints to the BBC, the broadcasting watchdog Ofcom and even the Metropolitan Police.

The Christian Institute’s Mike Judge said: “It is inconceivable that a prominent politician would retain his position on the Conservative front bench if he joked on television about murdering a supporter of gay marriage.”

Defending his comments, Mr Duncan, who hopes to be Home Secretary if the Conservatives win the next election, insisted: “Of course it was in jest. It is a comedy show after all. I’m sure Miss Prejean’s very beautiful and that if we were to meet we would love each other.

“I have no plans to kill her. I’ll send her a box of chocolates – unpoisoned.”

However, according to a reader of the homosexual news site Pink News who was in the show’s audience: “The BBC must have used canned laughter when screening the programme as the audience weren’t laughing that much. Everyone thought it was a really weird thing to say.”

Miss Prejean, who already holds the title of Miss California, came second in the Miss USA beauty contest earlier this month where she responded to a judge’s question about gay marriage.

She answered: “I believe that a marriage should be between a man and a woman. No offence to anybody out there, but that’s how I was raised.”

The judge who asked the question told ABC News: “She lost it because of that question. She was definitely the front-runner before that.”

He also said Miss Prejean has ‘half a brain’ and that he would have stormed onto the stage and ripped off her tiara if she had won.

However, the 21-year-old has stood by her comments.

“I was representing California. I was representing the majority of people in California,” she has since said.

Last year a majority of Californians voted to amend the state constitution to make it clear that only a marriage between a man and a woman is valid or recognised in California.