Cardinal Keith O'Brien described its implications as "grotesque" and akin to "Nazi-style experiments".
The medical academic Lord Winston hit back, claiming the Catholic Church knew about the experiments, but did "very little" to prevent them happening.
Cardinal O'Brien admitted making the remarks to gain publicity.
He said he did not see why people were offended.
In an open letter, Cardinal O'Brien said he was "appalled" that Gordon Brown was promoting the bill.
The Human Fertilisation and Embryology Bill, being discussed in the House of Lords, would allow cells taken from incapacitated adults and children on the basis of presumed consent to be used for embryo research.
Cardinal O'Brien wrote: "The grotesque implications of these procedures are utterly horrifying and fly in the face of all medical guidance on consent to research."
He said this behaviour was last seen under the Nazis, and urged the prime minister to urgently amend the legislation.
The Cardinal told BBC Scotland he wanted people to pay attention to the issue, adding: "Yes, I want publicity and I use strong language so that I'll get publicity."
He said he did not intend to offend anybody with his Nazi comments."Christian people might be offended as well, because of the suffering of some Christian people as well as the terrible suffering by the Jewish people, but I don't see why anybody should be offended by the language I use," Cardinal O'Brien said.
Lord Winston said the Nazi comments were unacceptable, adding that extreme remarks polarised opinion and did not do the Catholic Church justice.
The Labour peer told BBC Scotland: "It might be worth reminding the Cardinal that, actually, the Catholic Church knew about the Nazi experimentation, even before the war, not just after it, and did very little to prevent it from happening."
Catholic Labour MP Jim Sheridan accused his church of "scaremongering", and said a more measured approach was needed.
The MP for Paisley and Renfrewshire North said Cardinal O'Brien's remarks were "very far from reality", adding: "Winding people up is not consistent with the teachings of the Catholic Church."
Scottish Secretary Jim Murphy told BBC Scotland's Holyrood Live programme: "The Cardinal is more than entitled to his opinions - I don't agree with some of the specifics - but I have enormous personal respect for him and other church leaders in Scotland."Mr Brown previously said the bill would improve research into many illnesses, while other supporters said hybrid embryos could lead to cures for diseases, including Multiple sclerosis and Alzheimer's.
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