Labor's decision to bring on a same-sex marriage bill has sparked turmoil in the Liberal-National coalition.
Opposition Leader Bill Shorten brought a bill to parliament on Monday to redefine marriage as being between two people rather than a man and a woman.
While Labor, the Greens and marriage equality lobbyists want a speedy result, the coalition's joint party room meeting did not consider the matter on Tuesday.
A Liberal Party meeting did not go ahead because of Senate estimates and the Nationals are standing by their policy to retain the status quo.
The next Liberals meeting is not due until June 16.
Assistant Treasurer Josh Frydenberg caused ructions when he declared on ABC TV that he supported same-sex marriage laws being passed this year, most likely via a cross-party agreement.
Liberal MP Sarah Henderson backed Mr Frydenberg, saying the change should be made out of a sense of "compassion, equity and justice".
ACT senator Zed Seselja said he did not believe there was enough support among his Liberal colleagues for a free vote and ministers should stand by the party's present position opposing same-sex marriage.
"I don't think that's helpful," Senator Seselja said of Ms Frydenberg's comments.
Queensland LNP MP George Christensen said speaking publicly against coalition policy was disloyal.
"Whether ministers and parliamentary secretaries like it or not, the Liberal-National coalition's policy is to support the retention of the definition of marriage as outlined in the Marriage Act," he said.
Liberal senator Cory Bernardi said his party's conservative supporters would be "desperately disappointed" if the policy changed "because of pressure from the Labor Party and a few activists".
Nationals MP John Williams said the issue had been introduced at several party conferences and voted down each time.
"It's National Party policy to keep the status quo and that's exactly where I will be going," he said.
The latest Essential poll, released on Tuesday, found 59 per cent support for same-sex marriage, with 30 per cent opposed and 11 per cent undecided.
Support was weakest among over-65s, with 43 per cent in favour and the same proportion against.
A third of voters said they would be more likely to vote for a candidate who supported the change, while 22 per cent were less likely and 40 per cent felt it would make no difference.
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