The Greens are heaping pressure on Prime Minister Anthony Albanese's government to double funding to the national housing and homelessness agreement to $3.6 billion a year.
Under the proposal, states and territories would also be offered a share of an extra $2.5 billion a year in exchange for freezing and capping rent increases.
The Parliamentary Budget Office estimates doubling the agreement's baseline funding would cost $40 billion over a decade and another $28 billion for the rent freeze incentive.
The government provided states and territories with $1.7 billion as part of a one-year extension of the agreement but it expires on June 30.
Discussions on a new deal have been held in the lead up to the May 14 federal budget.
Data from the Australian Institute of Health and Welfare shows 37,392 women and children experiencing domestic and family violence sought long-term housing assistance in 2022/23.
Of those clients, 1365 (3.7 per cent) were provided long-term housing.
In 2021, a report commissioned by Everybody's Home estimated the dearth of long-term social housing was leading to 7690 women a year returning to violent partners and another 9120 becoming homeless.
Greens housing and homelessness spokesman Max Chandler-Mather said it was national disgrace tens of thousands of women and children fleeing domestic violence were being turned away.
"Doubling housing and homelessness funding would help ensure every woman escaping domestic violence receives accommodation and support, it's as simple as that," he said.
National cabinet on Wednesday signed off on a plan to give women escaping violence a $5000 payment, following a spike in the number of women killed at the hands of men.
The program will be a permanent extension of a previous trial set up under former prime minister Scott Morrison's government.
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