The government needs the support of the Greens and two crossbenchers to pass its $10 billion housing fund, which it says will generate 30,000 social and affordable housing properties in its first five years.

But the Greens as well as independent senators have criticised the bill for not going far enough to address a national shortage of social and affordable housing.

Greens housing spokesperson Max Chandler-Mather said the delay will force the Albanese government to consider rental support and direct social housing investment.

"Now with the bill being delayed for about a month the government has a chance to come to the table and actually negotiate," Mr Chandler-Mather told a housing rally at Parliament House on Tuesday.

The Greens want to use negotiations to introduce a national freeze on rent increases for a two-year period, at least $5 billion of investment in public and community housing and $1 billion for First Nations housing.

"So far, there has been no offer of direct investment in public and affordable housing, and we are going to continue to push the government on that," Mr Chandler-Mather said.

"We know that it has not yet been ruled out and we're going to keep pushing for the next month."

The Greens MP spoke alongside the Construction, Forestry, Maritime, Mining and Energy Union national secretary Zach Smith, as well as senators David Pocock and Lidia Thorpe, and representatives from ACT Shelter and the ANU Students Association.

"Our union will campaign to see more investment in social housing," Mr Smith told reporters.

"Yes, we're part of the broader Labor movement, but we will always stand up for our members, for working people and society's most vulnerable."

The union representing construction workers said the government needs to invest $290 billion into social and affordable housing over the next two decades.

It is understood senators Pocock, Thorpe and Jacqui Lambie have also been meeting with Housing Minister Julie Collins regarding the fund.

Senator Pocock said he will continue to ask for a more ambitious commitment to social and affordable housing.

There is a shortfall of 3100 public houses in the territory, with those on the list waiting an average of five years for accommodation.

Canberra is also Australia's most expensive capital city to rent in, with a median weekly rental value of $681.

READ MORE:

Senator Pocock has said the ACT would only receive funding for 540 new homes under the fund, based on a per capita breakdown.

"Here in the ACT even with the Housing Australia Future Fund, we are facing a net loss of affordable housing," he said.

Ms Collins on Tuesday said senators opposed to the fund were saying "no to getting homes on the ground for people that need it most".

"We know on Census night in 2021, almost 123,000 Australians were homeless. 123,000 Australians without a safe place to call home," Ms Collins said.

"We also know that we need to change the levers and we need to work with states and territories, which is what the Housing Australia Future Fund is all about."

Our journalists work hard to provide local, up-to-date news to the community. This is how you can continue to access our trusted content: