The Greens have offered to compromise further on the government's signature housing bill to put an end to a stalemate in the Senate, but the federal government looks unlikely to take up the offer.
The $10 billion Housing Australia Future Fund has been stalled in the Senate for weeks as the government has struggled to find enough support for it to pass.
The government plans for the fund to contribute up to $500 million each year to build up to 30,000 social and affordable homes over five years.
But the Greens demanded far more funding, saying the government should be spending closer to $5 billion each year to close the gap in the nation's housing shortfall, and arguing that the fund did nothing to help renters.
Greens housing spokesman Max Chandler-Mather told the ABC his party was prepared to halve that demand to $2.5 billion, still a five-fold increase over the government's policy, if the government also provided a $1 billion annual incentive for states to freeze rents.
"The shortage right now … is 640,000 social and affordable homes, and that is going to increase by 75,000 homes, and the government has said they can build up to 30,000 homes over the next five years," Mr Chandler-Mather said.
"So, really, what they're saying is — the crisis is going to get worse under their plan.
"Our point to the government is: this is one of the worst housing crises in this country's history. If they can find $30 billion a year for the Stage 3 tax cuts that sees every politician get $9,000 a year, why can't they find $2 billion for affordable housing and $1 billion for rental freezes?"
Mr Chandler-Mather said there was a current shortage in social and affordable homes of 640,000 set to grow by 75,000 in the next five years, and so the government's plan to build 30,000 homes under the fund would let the housing crisis worsen.
Housing Minister Julie Collins said the government had addressed "every single concern raised jointly by the Senate crossbench", and the Greens needed to stop delaying.
"Australia desperately needs the 30,000 new social and affordable rental homes the fund will deliver in its first five years," Ms Collins said in a statement.
"What we don’t need are proposals that won’t work, are not backed by evidence and would only make our housing challenges worse."
The federal government contends a rent freeze would be unlikely to work, pointing to evidence last week from the Reserve Bank governor that it would distort the supply side of the housing market, potentially damaging investment.
Ms Collins has also previously argued the Housing Australia Future Fund would not operate in isolation.
The fund would sit alongside a lift to Commonwealth Rent Assistance, $575 million made available for the National Housing Infrastructure Facility to immediately invest in rental homes, and a commitment to invest $350 million to deliver 10,000 rental homes over five years, as part of a national deal with the states and territories.
Greens leader Adam Bandt said his party had shifted and it was time for Labor to follow.
"If Labor backs a rent freeze and guarantees real money for more housing, the Greens will pass Labor's bill," Mr Bandt said in a statement.
