Opponents of gay marriage are being treated in a similar way to the Jews at start of Nazi rule in Germany, the former Archbishop of Canterbury claimed yesterday.

In highly controversial remarks at a rally of anti-equality campaigners, on the fringes of the Conservative Party conference in Birmingham, Lord Carey suggested that the intolerance of those in favour of gay marriage risked turning Britain into a totalitarian state. He also warned that gay marriage was a step on the "slippery slope" to the polygamous relationships of traditional Mormons.

Asked about people who described those who campaign against gay marriage as bigots, Lord Carey suggested such comments could be the start of something more sinister. "Let us remember the Jews in Nazi Germany," he said. "What started against them was when they started to be called names. And that was the first stage towards that totalitarian state. We have to resist them. We treasure democracy. We treasure our Christian inheritance and we want to debate this in a fair way."

Lord Carey's remarks drew criticism from Jewish groups who described his comments as "completely out of proportion". Rabbi Laura Janner-Klausner said: "Invoking Nazi persecutions and the Holocaust does not contribute towards a sensible debate. Lord Carey's choice of words is deeply regrettable and completely out of proportion; resorting to such hyperbole undermines his argument."

The equality rights group Stonewall also condemned Lord Carey. Chief executive Ben Summerskill said: "The fact that Lord Carey and others are resorting to this vitriolic language suggests they have lost the argument."

Lord Carey pointed to an application from a man in Sao Paulo, Brazil, for a civil union with two women, saying: "That is getting into a Mormon-style relationship."

He said that from "time immemorial", marriage had been between a man and a woman: "Same-sex relationships are not the same as heterosexual relationships and should not be put on the same level. Why does it feel to us that our cultural homeland and identity is being plundered? I have the highest of regards for David Cameron. I hope, in the months to come, he may have the courage to back down."

The former Tory MP Ann Widdecombe told the rally: "The real bigots...are those who believe that those who dissent have no right to do so and that the state should silence them." The event, attended by 500 people, was addressed by the Conservative MP David Burrowes. Senior Tories who have expressed concerns at the gay marriage legislation stayed away.