Bill Shorten has pointedly reminded Malcolm Turnbull of the prime minister's first anniversary as Labor brought on a bill to allow same-sex marriage.
This week marks one year since Mr Turnbull toppled Tony Abbott for the Liberal leadership in the wake of concerns about 30 bad Newspolls in a row and fears of a faltering economy.
The prime minister has had to come to the defence of Abbott government decisions including a plebiscite on changing the Marriage Act.
As parliament returned for a four-day sitting, the Labor leader brought on a private bill to legalise same-sex marriage but flagged the opposition would support an alternative bill if the government brought on its own legislation.
"I say to the prime minister - this is an issue you said you cared about," Mr Shorten told parliament.
"You have been prime minister for a year now - you can get this done."
Mr Shorten said extending equality under the law to all Australians would show "parliament can lead and keep faith with the people".
Greens MP Adam Bandt moved a similar bill on behalf of crossbenchers, telling parliament the proposed plebiscite - which is expected to be discussed by cabinet on Monday - was unnecessary, hateful and hurtful.
"Funding a referendum that is not binding on this place is the equivalent of funding the schoolyard bully to go and insult other students," Mr Bandt said.
Details of the plebiscite, including whether public funding will be allowed for the yes and no cases, are expected to go to a coalition joint party room meeting on Tuesday.
Meanwhile, at a meeting on Monday coalition MPs were warned by Leader of the House Christopher Pyne not to miss any votes on the floor of parliament.
This followed the debacle of the first sitting week where three procedural votes were lost because Justice Minister Michael Keenan and other Liberal MPs left early without informing the whips.
Treasurer Scott Morrison said the meeting with Mr Pyne had been "very constructive."
Asked about the same-sex marriage bills, Mr Morrison said the government would put its election agenda - which included a plebiscite - to the parliament.
The treasurer is holding talks with Labor to pass an omnibus bill to save the budget more than $6 billion.
"That is a test for the parliament, but we are engaging those discussions practically, in good faith ... to get a result," Mr Morrison said.
In the wake of Labor senator Sam Dastyari going to the backbench over the Chinese donation scandal, the opposition has appointed ACT MP Katy Gallagher as manager of opposition business in the Senate.
The government is set to taunt Labor in question time over Senator Dastyari, as the opposition seeks to increase the pressure on Mr Turnbull over his leadership.
Former Abbott chief of staff Peta Credlin said the most urgent task for Mr Turnbull was to "get his mojo back".