Heels remain dug in a housing policy impasse the government says is delaying pathways to home ownership and building more dwellings.
The coalition and Greens are united in opposing the government's proposed Help to Buy and Build to Rent schemes, believing neither will make housing more affordable.
The prime minister rejects this as he ramps up pressure on the political rivals to pass his government's policy.
"When it comes to housing, we are building; the coalition and the Greens have been blocking," Anthony Albanese said in Canberra on Monday.
Help To Buy, introduced to the Senate on Monday, would reduce deposit requirements for first-home buyers via a government loan guarantee.
Similar schemes operate in Western Australia, the ACT, NSW and Victoria and Mr Albanese said the federal version should have "sailed through parliament".
Greens MP Max Chandler-Mather claims the proposal will drive up house prices for those who don't get access to the program.
Independent senator David Pocock said he wanted more households to be able to access the scheme each year and for it to run on an ongoing basis.
The government is also trying to pass Build to Rent legislation, which offers tax concessions to the sector with the aim of delivering more homes built for renting.
Mr Chandler-Mather said the changes would increase rents and give tax breaks to developers to build unaffordable apartments.
"Neither will give light at the end of the tunnel for the single mum right now choosing between feeding her kids or paying the rent," he told ABC Radio.
The Greens want a freeze and cap on rent increases, and tax handouts for developers phased out.
The legislation will not improve affordability, opposition finance spokeswoman Jane Hume says.
"All it will do is allow large corporations, and indeed the government, to own your home," she said.
The logjam has tested the patience of independent MPs Allegra Spender and Zoe Daniel, who called for constructive discussion on housing.
As debate continues, housing supply continues to lag well behind demand for sale and rental homes, according to the Urban Development Institute of Australia.
The institute's national president Col Dutton said the "extremely challenging" housing market highlighted by its quarterly index underscored the need for government policy to boost the supply of homes - and fast.
"Demand now sits at record highs, while housing supply remains at near a decade low with all jurisdictions recording either decreased supply or only marginal improvements," he said.
The first tranche of funds for the government's Housing Australia Future Fund and National Housing Accord programs are expected to deliver more than 13,700 new social and affordable homes nationwide, the federal government announced on Monday.
Construction on almost 40 per cent of the builds was expected to begin in the current financial year.
Mr Albanese said the programs would deliver social and affordable housing to those who needed it most.
Round one of Housing Australia Future Fund will unlock $9.2 billion of investment in social and affordable housing, and will include more than 1200 homes for women and children escaping domestic violence and older women at risk of homelessness.
