Treasurer Jim Chalmers says he's willing to work with states and territories to boost funding for housing.
The government still faces an uphill battle to get its $10 billion Housing Australia Future Fund through the Senate, with both the opposition and the Greens blocking the proposal.
While guarantees of 1200 homes for each state and territory have been secured, the Greens want a rent freeze and more immediate investment to solve housing shortages.
The housing fund, a signature policy of the government, would commit to building 30,000 new social and affordable homes.
Dr Chalmers said the government wanted to boost housing supply but was also open to negotiating with state and territory government on possible extensions of funding.
"Obviously (I'm) not going to pre-empt the conversations that we have with the states and territories or to nominate a number, we've indicated that we will be extending it, we'll work in the usual collaborative and cooperative way," he told the ABC's Insiders program on Sunday.
"It wouldn't be the best negotiating tactic to nominate a number today, but we said we're prepared to extend it."
The treasurer said a 15 per cent rise in Commonwealth rental assistance as announced in the federal budget was among ways to ease pressure for renters, rather than a freeze.
Greens housing spokesman Max Chandler-Mather said while it a positive sign the treasurer would look to boost funding to state and territories, a rent freeze was needed.
"Labor's housing bill doesn't guarantee a cent in funding for public and affordable housing, and does nothing for renters in the middle of the worst housing crisis we've seen in generations," he told reporters in Brisbane on Sunday.
"Every week they don't act, another renter will be evicted because they can't afford $150-$200-a-week rent increase."
Dr Chalmers said the Greens were playing games in holding up the housing legislation.
"Labor and a number of the crossbenchers are trying to build more social and affordable homes in our communities, and some parties - the Liberals and the Greens - are saying that they will vote to prevent that," he said.
"It's time for the Senate to end its political games and get on board."
Mr Chandler-Mather said the Greens were still willing to negotiate with the government on the bill.
"It beggars belief that the federal treasurer can't engage in good faith in a negotiation where the Greens have pointed out that in its current form, Labor's housing bill doesn't guarantee a cent in funding for public and affordable housing," he said.
"(The bill) does nothing for renters in the middle of the worst housing crisis we've seen in generations."
Shadow treasurer Angus Taylor described the housing fund policy as a Ponzi scheme, saying the number of houses being built would make no difference to the situation due to an expected rise in migration numbers.
"Labor's housing policy will make almost no relevant contribution to the numbers required here of houses over the coming years," he told Sky News.
"We need a proper plan, a managed approach to immigration. That is not what was offered in this budget."