The Church of England has backed the Catholic Church in its bid to be exempt from laws on adoption by gay couples.
Dr Williams said rights of conscience cannot be subject to laws
Catholic leaders in England and Wales say its teachings prevent its agencies placing children with homosexuals and they will close if bound by the rules.
Archbishop of Canterbury Rowan Williams and the Archbishop of York, John Sentamu, have written to Tony Blair.
They say "rights of conscience cannot be made subject to legislation, however well-meaning".
The Equality Act, due to come into effect in England, Wales and Scotland in April, outlaws discrimination in the provision of goods, facilities and services on the basis of sexual orientation.
Matter of conscience
The archbishops said many people who do voluntary work are motivated by religious beliefs.
They point out exceptions have already been made for those whose conscience dictates they cannot take part in certain work, such as NHS doctors unwilling to perform abortions.
"In legislating to protect and promote the rights of particular groups the government is faced with the delicate but important challenge of not thereby creating the conditions within which others feel their rights have been ignored or sacrificed, or in which the dictates of personal conscience are put at risk," they said.
Archbishop Sentamu, speaking on BBC Radio 4's Today programme, said: "The freedom of conscience cannot be made subject to legislation however well-meaning."
He said the Church was "absolutely" against discrimination, and also did not believe homosexuality was a sin.
But he warned: "When you over-legislate and intervene too much in people's private lives I think in the long run you end up with a statute being used to cure all ills, which it cannot."
The row over whether Catholic adoption agencies should be exempt from the change in the law, which would require them to work with gay couples, is said to have split the Cabinet.
It is understood that many Cabinet members are not prepared to concede on the issue, but the prime minister's official spokesman said he was not aware that any had threatened to resign over it.
On Wednesday evening a Downing Street spokesman said "no decision" had been taken on any exemption.
But he said he did not recognise any suggestion that the decision would be "kicked into the long grass" and said it was "ridiculous" to suggest Mr Blair had "caved in".
Communities Secretary Ruth Kelly, who is Catholic, is reported to be pushing for an exemption.
Ambition or faith?
Labour MP Stephen Pound, also Catholic, does not support a religious exemption and believes the adoption row has put Ms Kelly in a difficult decision.
"We seem to be living in a world where people who have strongly held views are somehow derided for that," he told BBC's World At One.
"In Ruth's case there is demonstrably a conflict. Is it right for us to expect someone to abandon everything they believe in because of the prevailing majority view? Does she abandon her ambition or her faith?"
The National Secular Society said that allowing an exemption for the Church would open the "floodgates for a never-ending series of demands".
Cardinal Cormac Murphy-O'Connor, the leader of Catholics in England and Wales, has asked that his agencies be allowed to opt-out of rules requiring that gay couples be considered as prospective adoptive parents.
But he has denied claims that he is using "blackmail" by saying Catholic agencies will have to close, if bound by the laws.