Independent senator Lidia Thorpe has thrown her support behind the Housing Australia Future Fund (HAFF) deal struck by Federal Labor and the Greens.

The deal, supported by the Greens and other crossbenchers, gave the government the numbers to ensure the $10 billion HAFF bill passed the Senate on Wednesday.

The Fund will use the interest accrued from a borrowed $10 billion to deliver 30,000 new social and affordable rental homes over the next five years.

Whilst in support of the agreement, Senator Thorpe said the deal was a "missed opportunity for renters and First Peoples".

"While I welcome the news that the legislation has passed, I am disappointed the Greens did not advocate for the recommendations of First Nations housing bodies and grassroots organisations," Senator Thorpe said.

"I want to express my profound disappointment that First Peoples, who are by far the most in need of housing, have been largely ignored and are once again left with next to nothing out of all this.

"We are in a housing and homelessness crisis, and First Peoples are the hardest hit by this crisis."

Senator Thorpe had previously advocated for an increase to the annual minimum spend, the introduction of legislated targets into the scheme for First Peoples housing, and the establishment of a First Peoples Housing Authority to work with the new National Housing Supply and Affordability Council, none of which were supported by government.

She said the legacy of housing poverty and deprivation continues to be a national shame.

"First Peoples should have been a priority population, yet instead the government has refused to introduce a target for First Peoples housing in the legislation. This was low hanging fruit when it comes to listening to First Peoples voices," she said.

"We deserve a housing system that is culturally safe, trauma informed and based on the principles of self-determination. Recent Closing the Gap findings have revealed the failure of governments to properly consult with our people."

The proud Gunnai, Gunditjmara and Djab Wurrung woman said she is looking to increase her pressure on the government to adequately address the housing and homelessness crisis.

"If the Albanese Labor government is serious about tackling the First Peoples housing and homelessness crisis, they will establish a standalone First Peoples Housing and Homelessness Plan, commit to growing and strengthening the community-controlled housing sector, and expand culturally safe tenancy support programs," she said.

The Opposition remained staunchly against the proposal.

South Australian Liberal senator Simon Birmingham said the fund would not adequately address the country's housing crisis.

"It's not going to generate the type of numbers of homes that will shift the dial in a market that is pressured (by) population and migration," he told Sky News.

Independent senator David Pocock and Jacqui Lambie Network senator Tammy Tyrrell were both in support of the bill.