The laws to set up the Indigenous voice referendum are expected to make it into legislation as federal parliamentarians return to Canberra for the next sitting fortnight.
The referendum, expected to be held between October and December, will enshrine constitutional recognition of Indigenous people and the voice to parliament.
The referendum has passed the lower house but debate could take days as senators have their say and seek amendments.
The Albanese government has also been locked in negotiations with the Greens to pass the $10 billion housing future fund through parliament.
The Greens have two key demands - a freeze or cap on fast-rising rents and more money for social and affordable housing than the maximum of $500 million that will flow from the fund each year.
The minor party is happy to negotiate on where the extra funding for public housing comes from - as well as the total sum - but wants a guaranteed yearly spend. One suggestion is to put aside money in the budget in case the fund's earnings fall short.
The party also wants to protect tenants from soaring rents and has been calling for an additional incentive fund of $1 billion to encourage states and territories to impose a two-year rent freeze.
A national rent freeze would be preferred but a cap on increases may be considered as an alternative.
The government has secured the support of key independents needed to wave the bill through the Senate and is now waiting on the Greens.
Treasurer Jim Chalmers said the government had been negotiating and cooperating with the crossbench for some time.
"The time has come to end the ambit claims and the political games and the vote for more social and affordable housing," Dr Chalmers said on Monday.
He said the fund was a key part of its housing policy but not the only component, with the government also opening up more funding to the National Housing Finance and Investment Corporation to support the construction of 7000 new social and affordable homes.
A range of other bills will be discussed over the week in relation to healthcare, education, childcare, infrastructure, environment, the arts and to prohibiting hate symbols.
