Laws to set up the Indigenous voice referendum are expected to pass federal parliament over the next sitting fortnight.
With the lower house having passed the referendum bill in the previous sitting, the debate shifts to the Senate.
The referendum, scheduled to be held between October and December if the bill passes, will ask Australians whether they want to change the constitution to recognise Aboriginal and Torres Strait Islanders and set up a voice to parliament and government.
The bill is expected to pass the Senate but the debate could take days as all senators have their say and a number of them seek to move amendments.
The Senate is also scheduled to deal with laws to set up a $10 billion Housing Australia Future Fund, a key Labor election promise.
But talks continue between the government and Greens on a compromise.
The Greens want the government to offer the states and territories $1 billion a year for housing and homelessness services in exchange for a two-year freeze on rent increases, ongoing rent caps and improved renters' rights.
As well, Labor is being asked to guarantee at least $2.5 billion a year is spent on public, community and affordable housing, starting now.
Housing Minister Julie Collins said she had addressed the specific concerns of eight crossbenchers and was continuing "good faith discussions".
She also highlighted her signing of a new investment mandate for the National Housing Finance and Investment Corporation to make available an extra $2 billion from July 1, supporting 7000 new social and affordable homes, and work with the national cabinet on renters' rights.
It has been speculated the possible voting down of the housing bill could give Prime Minister Anthony Albanese a double-dissolution election trigger.
"I'm not contemplating an early election," Mr Albanese told a business forum in Sydney on Friday.
Former NSW Liberals president Maria Kovacic will be sworn in as senator on Tuesday to replace the late Jim Molan.
The lower house will deal with budget bills and environmental laws, while Attorney-General Mark Dreyfus will introduce a bill to ban the sale of Nazi memorabilia on Wednesday.
MPs will also debate a bill to ensure the Australian Medical Association no longer has to approve the director of the Medicare oversight body.
Coalition senators are expected to pursue minister Katy Gallagher over her knowledge of Brittany Higgins' rape allegations and whether she misled a Senate estimates hearing in June 2021.
Issues relating to Queensland are tipped to be a focus of question time with the major parties battling it out for the Fadden by-election on July 15, triggered by the resignation of former minister Stuart Robert.
It will be the last sitting fortnight before a five-week winter break.
