Prime Minister Anthony Albanese is seeking advice on the next steps – including dissolving parliament and calling an early election – if the Greens continue to dig in and delay a signature housing proposal.

The Greens teamed up with the Liberal Party in the Senate on Monday to delay the proposed $10 billion housing future fund until October.

They cited a lack of support for renters and said the delay would allow Labor to negotiate rent reforms with state and territory leaders.

On Tuesday, Mr Albanese told his party room colleagues the Greens’ action to defer the bill could be taken as a “block” and the government was seeking advice.

The constitutional advice could relate to the triggers required for a double dissolution of parliament, resulting in an early election.

Mr Albanese said the Greens brought a “juvenile student politics approach” to negotiations that needed to be exposed.

“They say they tried to push us further; the reality is they blocked it,” he said.

“Their proposal would result in less supply and less investment, which would make the problem worse.”

Asked if the legislation would be brought back, Housing Minister Julie Collins said the government would look at “all the options available”.

“What we want to do is get on with the job of delivering homes,” she said.

“We’re working with our partners in the states and territories, local government and the community housing sector to deliver homes each and every day, and we’re going to continue to do that.”

But a vote on the bill in October is now uncertain, with Ms Collins declining to say if the government would bring back the legislation for further debate.

“We’re looking at what we’re doing, what options are available to us,” she said.

“You saw that last weekend when we announced our $2 billion Social Housing Accelerator. What we want to do is get on with building homes.”

Also on Tuesday, a Greens party room meeting was told the decision to defer the housing bill was “unprecedented”. Greens leader Adam Bandt said the ball was firmly in the government’s court.

“If the government and Labor act on rising rents and out-of-control rent increases, then this bill can pass the Senate when it comes back,” he said.

“What position the Greens take when the bill comes back will be influenced in large part by what governments around the country, including the prime minister, are prepared to do on soaring rents.”

Mr Bandt rejected suggestions what the Greens did amounted to the first step towards a double dissolution trigger.

The Greens have called for a parliamentary inquiry into rent affordability and rights, with an interim report to be published in September.

The government has separately announced a $2 billion commitment for social housing, to be shared among the states and territories.

Greens housing spokesman Max Chandler-Mather said the extra funding was a sign the government was willing to act on Greens’ demands.

Independent senator David Pocock said it was disappointing the Greens and coalition delayed the legislation after months of negotiations where the government made concessions.

“I appreciate that the Greens want to try to get more out of this,” he said.

“But my view is after months of drawn-out negotiations and some concessions from the government, it is time to either vote for the legislation or vote against it and send them [the government] back to the drawing board.”

“At the moment, we are just kicking the can down the road … stringing this out. No one wins here.”

Senator Pocock said 300 people every day nationwide were denied requests for emergency accommodation.

He also urged the government to keep talking with the Greens to find a resolution.

“The government should absolutely be trying to get a deal on this,” he said.

Advocates called on the Greens to support the legislation in its existing form, warning Australia faced a housing crisis.

-with AAP