Prime Minister Tony Abbott has indicated he won't be supporting Labor's offer of bipartisanship on Bill Shorten's same-sex marriage bill.
The opposition leader has given the government the opportunity to second the bill that he is due to introduce to parliament on Monday, rather than Deputy Leader Tanya Plibersek.
"I've made it very clear that while this is an important issue the government has an absolute focus right now on getting the budget measures through parliament," Mr Abbott told reporters in Sydney on Sunday.
Queensland Liberal Warren Entsch, a supporter of gay marriage, will not co-sign Mr Shorten's bill.
But he has told Fairfax media he has agreed to meet with Mr Shorten after the budget sittings that end on June 25, to try and come up with an "all parties" solution.
Confirmation was sought from Mr Entsch's office.
THis afternoon thousands rallied in Sydney for a free vote when Labor's same-sex marriage bill is introduced to federal parliament on Monday.
Tanya Plibersek told the cheering crowd it was time for change.
"This is the last piece of unfinished business," she said of gay and lesbian rights.
Ms Plibersek said a bipartisan approach to the bill would give it a much greater chance of succeeding, especially if someone in the coalition seconded it.
"This is a matter that transcends politics," she said on Sunday.
