The Albanese government is ratcheting up the pressure on the Greens over housing, as it prepares for a renewed push on a signature bill.

Legislation for the $10 billion Housing Australia Future Fund will be back before parliament when it returns next week.

The bill stalled in the Senate before the winter break after the Coalition and Greens teamed up to sink it, delaying further debate until at least October.

On Friday, Prime Minister Anthony Albanese said the bill – a key election pledge – should be passed to avoid a double dissolution election. He urged Greens leader Adam Bandt to “exercise responsibility”.

“You have the Coalition, One Nation and the Greens in the new no-alition, a no-alition saying no to improving housing affordability,” he said.

“People who are in positions of authority – and I say to Adam Bandt, he needs to exercise responsibility over his party and make sure that they vote for this bill and get this started.”

The fund would aim to build 30,000 homes in five years with $500 million being spent on affordable and social housing each year.

However, the Greens say it offers too little for renters. They want a rent freeze, along with a larger investment each year for housing.

Mr Albanese said the government had a mandate to implement the fund.

“I don’t anticipate that there will be an election this year. But quite clearly, we have a mandate for this. We want this to be passed. The way to ensure that this doesn’t provide a trigger is to pass the legislation,” he said.

“We don’t want to play politics with this. We want this to build additional social housing.

“I know the difference that a secure roof over my head, and my mum’s head, made to my life. It is important that this bill be passed.”

Earlier, Mr Albanese said the plan represented a record investment by a government “and what the Greens are doing is standing in front of that, having this rhetoric about refusal to negotiate”.

“This is all about politics, and quite clearly, if this legislation is passed, there’ll be more investment in social housing. You can’t say you’re for it and then vote against it,” he told ABC radio.

He said the Coalition had never supported public or social housing.

“The Coalition, of course, don’t really support public and social housing – they never have. They never have, and at least I guess they’re upfront about it,” he said.

“For the Greens political party, that say that they care about social housing, that they care about affordability, to be blocking this is quite absurd.”

Greens housing spokesman Max Chandler-Mather was unflinching on Friday. He said the party had given ground in the dispute, and momentum was growing for more action on issues such as rent freezes.

“That doesn’t mean we’ll get everything we want but I think it’s irresponsible of the government to try to force the bill back on for a vote when they refuse to make a single change,” he said.

“The public didn’t vote to give them a majority in the Senate and they should negotiate with us and not go to the Parliament and say it’s their way or the highway – especially when their way is more people waiting for public and affordable housing and locking in unlimited rent increases when we know already millions of renters are doing it tough.”

Earlier, Mr Chandler-Mather said some of Labor’s more than $20 billion surplus could be set aside for housing.

“We’re not asking for the world. We’re asking for a small amount of the budget surplus, $2.5 billion, to go towards public and affordable housing,” he told Sky News Australia.

Deputy Prime Minister Richard Marles downplayed suggestions the bill could be used as a double dissolution trigger, giving the government room to call an early election, if the Greens and the Coalition rejected it for a second time.

“This isn’t about elections, this is about getting more housing,” Mr Marles told ABC Radio on Friday.

“This is about making sure that we get a much greater supply through the $10 billion Housing Australia Future Fund.”

A double dissolution can be called if a piece of legislation is defeated twice in the Senate,. It means all seats in the upper house would be up for election instead of half, as normal.

Acting Opposition Leader Sussan Ley said Labor’s move on the housing fund bill showed arrogance.

“The policy does not stack up and meanwhile their economy-wrecking approach is making it more and more expensive to build a home,” she told Seven’s Sunrise program.

“What we need now is an urgent plan to tackle inflation, not threats about an early election.”

Housing Minister Julie Collins said the government would use every opportunity to pass the legislation.

“Every day of delay is $1.3 million not being spent on housing. So, we want to get these built,” she told Triple M radio.

“We want to reintroduce it. We want to get this bill done so we can get more homes on the ground.”

Earlier this week, the construction union launched a major campaign for a super profits tax on Australia’s richest companies to pay for social housing. It was quickly ruled out by Mr Albanese.

-with AAP