In a dramatic intervention, former defence minister Kevin Andrews backed church leaders, rather than the Prime Minister, in a dispute over whether Mr Turnbull promised taxpayer support to run the campaign against same-sex marriage.

The stoush comes as the Coalition's most long-standing supporter of same-sex marriage, Queensland MP Warren Entsch, called for Attorney-General George Brandis to be more transparent about the plebiscite process and work more closely with Labor.

Cabinet is set to debate the mechanism for the plebiscite on Monday before a party room debate on Tuesday.

Senator Brandis is expected to recommend against public funding in his cabinet submission, but conservative MPs are adamant it is essential to ensure both sides are given an fair hearing in the debate.

The Anglican Archbishop of Sydney, Glenn Davies, has said Mr Turnbull gave an "unambiguous" offer to provide taxpayer funding at a meeting in February, a claim backed by Australian Christian Lobby director Lyle Shelton.

Mr Turnbull and his senior aides at the meeting strongly deny making such a promise.

Mr Andrews, who was demoted from cabinet by Mr Turnbull last year, told Fairfax Media: "The Prime Minister's statements were clear that there would be a quantum of public funding for a yes and no campaign similar to a referendum.

"That is what I expect."

Asked if he believed Mr Turnbull had made this commitment to the public or to religious leaders, Mr Andrews said: "Both."

Liberal senator Cory Bernardi said "people will make up their own minds" about whether they believe Mr Turnbull or the church leaders.

"If a promise is made it has to be honoured," he said. "We don't want the plebiscite to be dominated by money wealthy individuals overseas."

Tasmanian senator Eric Abetz, a former Senate leader, said: "I am sure that nobody, when we first discussed the plebiscite, thought there would not be equal public finding for both sides.

"With a change as fundamental as changing society's basic foundational institution, there is an imperative that the arguments be able to be put. That requires funding."

Senator Abetz said each side should receive $10 million to make its case.

But Mr Entsch said he was "vehemently opposed" to public funding.

"We are giving the churches the plebiscite they want, don't come asking for money," he said.

Asked if Senator Brandis was doing a good job on the plebiscite, Mr Entsch said: "I want him to be more transparent, more open, more inclusive.

"I have no doubt the Attorney-General is committed to making it happen but I want to see him work with everyone. I want to see him talking to the other side about their views.

"Rather than having everyone second guessing about what may or may not happen, reassure them and take them on the journey with you."

Fairfax Media has been unable to find any definitive public statements by Mr Turnbull promising public funding. During the election campaign, he said if there was to be taxpayer support it would be on a "strictly equal" basis, a position he repeated on Sunday.

Senator Brandis, who had discussed details of the plebiscite with Labor's Mark Dreyfus, said the issue would be considered "very soon" by cabinet.

Labor marriage equality spokeswoman Terri Butler said the plebiscite was "going from bad to worse" and called on Mr Turnbull to ditch the idea.