Opponents say the bill will lead to 'Frankenstein'-style experiments
Gordon Brown says Labour MPs will get a free vote on the most controversial parts of the new embryology Bill.
The MPs will be able to follow their consciences in three areas - including allowing scientists to create embryos with human DNA and animal cells.
But the prime minister expects all Labour MPs to back the whole bill when it comes to the final Commons vote.
The PM offered the deal after warnings that some Catholic Labour MPs and cabinet ministers were ready to rebel.
Welsh Secretary Paul Murphy, one of three Catholic cabinet ministers expected to rebel, has told the BBC he is satisfied with the compromise and will vote with the government on the entire bill.
Defence Secretary Des Browne is also thought to be satisfied with the offer of a free vote on the most controversial parts of the Bill but has not said how he will vote on the legislation as a whole.
Transport Secretary Ruth Kelly was not available for comment.
The Human Fertilisation and Embryology Bill is designed to bring existing laws on fertility treatment and embryo research into line with scientific advances.
The three areas where Mr Brown said there would be free votes during the passage of the bill through the Commons are:
- Preventing fertility clinics from refusing treatment to single women and lesbians - under current legislation clinics must take account of the welfare of the unborn child including "the need for a father". This will be replaced by the "need for supportive parenting".
- Creating a child with the correct tissue match to save a sick brother or sister.
- Creating so-called hybrid animal/human embryos to aid stem cell research.
In his Easter sermon at the weekend, the leader of the Scottish Catholic Church, Cardinal Keith O'Brien, described the proposed legislation as a "monstrous attack on human rights, human dignity and human life", adding that it would allow experiments of "Frankenstein proportion".
In response to Mr Brown's compromise, his spokesman said it was "better late than never", however the bill still contained many "deeply troubling proposals".
Speaking at the launch of Labour's local election campaign, Mr Brown said: "I do believe that in stem cell research we have the power in the future to treat and to cure some of the diseases that have afflicted mankind for centuries."
Embryonic stem cell research "holds the key" to advances in the treatment of Alzheimer's, Parkinson, cancer and heart disease, he said.
"I have always said that although I attach huge importance to this legislation - to save lives and helping to cure and treat diseases - we respect the consciences of every member of Parliament as they decide how to cast their vote on this," he said.
"On the three issues where, for the first time, these ethical issues are being debated in Parliament in this new way... exercising your conscience will mean for Labour Party members a free vote.
"But the bill itself cannot be subject to a free vote because there are so many other changes that I believe are necessary as part of building up the research framework of our country and, of course, creating the right ethical framework for the development of embryo research."
Mr Brown said the government planned to ban so-called "designer babies" and was taking action "to ban in a large number of instances, experimentation with animal embryos".
Conservative leader David Cameron is allowing his MPs to vote with their conscience on the bill.
Health Minister Dawn Primarolo has said she is confident concerned Labour backbenchers can be won over by Mr Brown's compromise offer.
Labour MP Claire Curtis Thomas said she would rebel if the controversial measures remained in the bill, saying it was "primarily moral question and at the end of the day, I have to answer to my conscience".
But Fellow Labour MP Andrew Mackinlay backed Mr Brown's offer: "This is very welcome and some common sense has now prevailed."
Lib Dem science spokesman Dr Evan Harris said: "I am confident that more opposition MPs will support these measures than Labour MPs opposing them and that there will be a large majority - since I personally support embryo research I welcome that."