Housing Minister Julie Collins poured cold water over the suggestion to dump the fund model in favour of direct investment into housing on Sunday as negotiations over the key Labor election promise continue.
"The whole point of the fund is that it's there in perpetuity so that institutional investors, community housing providers have certainty that this funding will be available each and every year to leverage more investments, to get more homes on the ground," Ms Collins countered.
The Greens have been fighting for more ambition from the government than the $10 billion Housing Australia Future Fund, which will yield up to $500 million a year in earnings that will be spent on affordable and social housing projects.
The party has pared back its demands but still wants the government to tackle immediate rental stress and to commit $2.5 billion a year to purchase existing properties for social housing.
The Senate is scheduled to deal with the housing fund laws during the upcoming sitting fortnight.
Ms Collins told Sky News the government was still "happy to have discussions right across the parliament".
She also stressed the housing fund was not the government's only measure to address affordability challenges.
The government has signed 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.
The Commonwealth is also working with the national cabinet on renters' rights.
The Greens have been calling for a rent freeze or cap but the housing minister said the federal government did not have that power.
Ms Collins said this fell under the remit of state and territories and some had already ruled it out.
"What we have done is put renters' rights on the national cabinet agenda," she said.
"We're working with states and territories to have more consistency across the country around what rights renters actually have, so that renters do know their rights."
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