The DUP leader argued that Stormont was the correct place to deal with the topic of abortion in Northern Ireland.
The PM said the embryo research bill was a matter for the Commons and would be the subject of a free 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. +++++++++++++++++++++++++++++++++++++++++++++++++++
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