Anthony Albanese has accused the Greens of deliberately holding up a $10 billion housing fund so the minor party can campaign on poverty issues.

The prime minister’s critique in parliament came as the Greens argued their decision, in league with the coalition, to pause debate on the fund legislation until October was achieving positive results.

Mr Albanese said the Housing Australia Future Fund, which would build 30,000 new social and affordable homes, was supported by many housing and homelessness organisations.

“For the coalition, they’ve never supported social housing and they say ‘no’ to everything in this parliament,” he told parliament on Wednesday.

“(But) for the Greens … this isn’t about the Australian people, this is about them.

“They want the issue, not the outcome.”

He quoted an article by the Greens housing spokesman Max Chandler-Mather who wrote the “parliamentary conflict helped create the space for a broader campaign in civil society”.

Allowing the bill to pass would “demobilise the growing section of civil society that is justifiably angry about the degree of poverty, and financial stress that exists in such a wealthy country”, the article read.

“They want people to stay in poverty so they can rally against it,” Mr Albanese said.

Asked by Peter Dutton whether this would mean Labor would reject Greens preferences at the next election, Mr Albanese accused the opposition leader of relying on One Nation and United Australia Party preferences.

Greens leader Adam Bandt earlier said his party had succeeded in forcing the government to provide a further $2 billion for social housing last weekend and making other concessions on the bill.

This provided some hope the government would also shift on rent controls, in a deal with the states and territories via national cabinet.

Mr Bandt said he was not concerned about the government potentially using the blocking of the bill as a double dissolution trigger for an early election.

“We’re not talking about an early election, we’re talking about renters,” he told ABC radio.

“And just like Labor changed their mind on spending for housing, we want Labor to take the rental crisis seriously.

“As part of an agreement with the Greens, the Labor premier in Victoria is now saying they’re looking at rent caps and rent controls, and in the ACT where the Greens are in power with Labor there is a limit on how much rents can rise by.”

NSW Premier Chris Minns said he was concerned a rent cap would result in most private rentals jacking up prices out of fear fees would be locked in for the next three years.

“I’m not going to bring in a policy that international experience indicates doesn’t work, to solve a Senate logjam,” he said.

“If I thought a rent freeze to be put in place would work, I’d do it, but I don’t think it would.”

Housing Minister Julie Collins told parliament every day of delay on the fund legislation would mean $1.3 million not spent on housing.

Independent senator Jacqui Lambie, a supporter of the bill, said more children would be sleeping in cars with their parents because of the delay.

Opposition housing spokesman Michael Sukkar said the government’s social housing spending was a “rushed” announcement done to placate the Greens.

“Unless you identify the projects … I fear that $2 billion will just end up being subsumed into state and territory housing budgets, there won’t be any additional housing,” he told Sky News.

– AAP