Religious leaders were concerned that the resistance to gay weddings in church could be interpreted as a breach of the European Convention on Human Rights, which is now being incorporated into British law.
But the Government will today announce an amendment to the Human Rights Bill to ensure that courts recognise "the importance of the Convention right of freedom of thought, conscience and religion".
The amendment follows discussions between Mr Straw and church leaders. A Home Office spokesman said: "The amendment that the Government has tabled addresses the church's concern about the potential effect of the Human Rights Bill on religious organisations."
Bishops and religious leaders have already inflicted three defeats on the Government in the Lords amid claims that the new laws could lead to changes over church policy on homosexuality and education. It was further feared that the legislation could force churches to allow divorcees to remarry in church.
The Roman Catholic church was concerned that it might be challenged on sex discrimination grounds by women who were prevented from becoming priests.
Another amendment, this time to the Education Bill, will also be announced today to address the concern of religious leaders that the new laws might render them powerless to prevent atheists teaching at church schools. News of the amendments prompted speculation of a political clash between Mr Straw and the Lord Chancellor, Lord Irvine of Lairg, who was understood to have thought that such changes were unnecessary.
But yesterday the two departments quickly closed ranks. A spokesman for the Lord Chancellor's Department said the amendments had been "fully discussed and agreed" between the relevant ministers.
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