Organised by the Bishop of Wangaratta, John Parkes, the bishops say Senator Smith's bill should be approved as it stands.

"It preserves the fabric of our anti-discrimination laws, which have been developed over half a century," they say. "These give expression to democratic values of equality and fairness. It also accords fulsome recognition of the religious rights and freedoms that underpin a democratic, plural and multicultural society."

The letter points to a deepening split inside the Anglican church over same-sex marriage.

Sydney Archbishop Glenn Davies was a strong backer of the "no" campaign, donating $1 million to that cause during the three-month postal survey campaign and describing Senator Smith's bill as "wholly inadequate". And the head of the church in Australia, Archbishop Philip Freier, voted "no" in the survey and has been among those calling for strong religious protections in the bill.

Mr Turnbull says the amendments to the Smith bill he intends to support are "belt and braces" changes to confirm protections already present. They would guarantee charities will not be affected and allow civil celebrants to refuse to solemnise gay weddings.

"A lot of the amendments we're talking about are really providing assurance that things that are unintended consequences are not going to occur," he told Sky News.

Another change would make it clear "there is nothing in the bill that prevents or inhibits or hinders anyone from expressing their views about what is the morally right form of marriage", Mr Turnbull said.

A further range of amendments was moved by conservative MPs in the Senate last week but voted down. Labor voted as a bloc on all amendments and had enough support from Coalition moderates and the crossbenches to ensure the bill passed in its original form.

It is widely believed those who want Senator Smith's bill passed without change will also have the numbers in the lower house. Labor is expected to continue to vote as a bloc against amendments, with the support of several crossbenchers and the Liberal MPs who co-signed the bill: Tim Wilson, Warren Entsch, Trevor Evans and Trent Zimmerman.

Labor's Tony Burke said the House of Representatives should not seek to amend bills that had already passed through the Senate. He said it would be "absurd" if the bill failed to pass Parliament because the two chambers could not agree by week's end.