The government's housing fund remains deadlocked in the Senate despite latest compromise

In its most significant compromise yet, the government has agreed to scrap an annual cap on fund disbursements and replace it with a guarantee of annual disbursements of $500 million, indexed from 2029-30, and would include provisions empowering the treasurer and finance minister to increase the size of future fund payouts.

But Greens housing spokesperson Max Chandler-Mather has belittled the change and indicated that the government has not yet done enough to win his party's support.

"The Greens have bent over backwards to reach a compromise ... yet Labor has done nothing more than partly close a loophole that could have seen no money spent on housing at all," Mr Chandler-Mather said. "We will not be passing [the legislation] until they move on our two keys demands."

He said the Greens wanted guaranteed annual spending of between $500 million and $2.5 billion on public and affordable housing and a national rent freeze.

The government plans to have legislation to set up the fund voted on in the Senate during the current sitting fortnight and needs the support of the Greens and crossbench senators to have its legislation passed.

In a letter sent to four crossbench senators as well as Mr Chandler-Mather on Monday, Housing Minister Julie Collins detailed government changes to address concerns they have raised about the original proposal and urged them to support the bill.

In addition to scrapping the spending cap, Ms Collins said the government would ensure all funded homes meet design and energy efficiency standards, provide $200 million for repair and maintenance of Indigenous housing, work with the state and territories to develop a consistent definition of affordable housing and require the first review of the fund to be completed by the end of 2026.

"We urge you all to vote in support of the Housing Australia Future Fund, and the tens of thousands of rental homes it will help fund," the minister wrote. "Any further delay will mean people in need will wait longer for the homes the Housing Australia Future Fund will provide, including women and children fleeing domestic and family violence and older women at risk of homelessness."

But Mr Chandler-Mather said the changes did not go far enough.

"The Greens want to negotiate, but Labor is refusing to shift on the two key demands we've made clear for the last eight months," he said.

"What Labor is offering is a housing plan that won't spend money until 2024-25 then locks real term cuts for six years and does nothing for renters, when what we need is billions of dollars of investment in public and affordable housing immediately and an emergency freeze on rent increases."

Under the government's original plan, earnings from investments made by the $10 billion fund would be directed to finance the provision of social and affordable housing. It wanted disbursements capped at $500 million a year and claimed it would deliver 30,000 homes over five years.

The minor party has so far joined the Coalition in opposing the fund, arguing it falls well short of what is needed to remedy the severe shortage of social and affordable housing.

The Greens had demanded that the fund spend $5 billion a year on housing but recently halved that to $2.5 billion.

"When Labor can find $30 billion a year for the Stage 3 tax cuts, and $12 billion in tax concessions for property investors, it beggars belief that all Labor can find for housing is $500 million in 12 months time," Mr Chandler-Mather said.

Ms Collins told the senators and the Greens MP that the government had negotiated "in good faith" and called on the politicians to back the legislation when it is presented for a vote during the current sitting period.

"The $10 billion HAFF is the single biggest investment in social and affordable housing from a federal government in more than a decade, and will deliver tens of thousands of desperately needed rental homes across the country," Ms Collins wrote.

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The government has already secured the support of Jacqui Lambie Network senators Jacquie Lambie and Tammy Tyrrell after guaranteeing that each state and territory would receive a minimum of 1200 social and affordable homes each year.

And the government adopted independent ACT senator David Pocock's call for disbursements from the fund to be indexed from 2029-30.

The minister said Housing Australia, which will administer the grants from the fund, was already undertaking preparatory work so that work on new homes could begin as soon as the fund was established.

"The government expects Housing Australia will be in a position to enter into contracts for housing projects under the HAFF this financial year," she said.

But the government has so far baulked at Greens' demands for a national rent freeze and the idea has been rejected by Queensland premier Anastasia Palaszczuk.

Mr Chandler-Mather said the Greens had "shifted substantially [but] doing nothing for rent is not a response to the scale of the scale of the housing crisis".

He wants the government to offer the states and territories a $1 billion incentive to freeze rents.

Ms Collins said the government had delivered a 15 per cent increase in Commonwealth Rent Assistance, which was the largest boost to the payment in more than 30 years.