"We can see the light at the end of the marriage equality tunnel," Australian Marriage Equality spokesman Rodney Croome told reporters in Canberra.
But Liberal Democrat David Leyonhjelm, who has his own bill before the Senate, was dismissive of Labor's move.
"It's the same as the Greens bill in the Senate. What's the point? We need one that will pass, not grandstanding," he tweeted.
Greens leader Richard Di Natale challenged Mr Abbott to put the issue on the agenda of a joint meeting of the coalition parties on Tuesday.
But the prime minister says his priority is getting the budget through parliament.
"I accept that same-sex marriage is a significant issue," he told reporters in Canberra.
"But frankly, this government's absolute fundamental priority ... is the small business budget boost."
With the government in control of the lower house and its selection committee, it's unlikely there will be any time for a parliamentary debate before the winter break in late June.
Mr Shorten's bill might not even get to a debate as Mr Abbott has previously said the Liberal party room won't discuss the issue until closer to a vote on a suitable bill owned by the whole parliament rather than by one political party.
Mr Croome said if Mr Abbott was serious about supporting small business he should back same-sex marriage, citing a US study which showed gay weddings could provide a boost to the Australian economy of between $161 million and $600 million.
Parents and Friends of Lesbians and Gays spokeswoman Shelley Argent travelled to Canberra on Monday carrying 40 kilograms of letters from members of the public to federal coalition MPs and senators, urging them to end marriage discrimination.
"This country is really tired of the procrastination," she said.
- AP
