The Australian Greens have cited research conducted by the federal Parliamentary Library to boost their case for a national rent freeze, as tense negotiations over the federal government’s signature housing investment fund continue.

The government has already failed once to get its $10 billion fund through the Senate.

Prime Minister Anthony Albanese has threatened to dissolve both houses of parliament and call a double dissolution election if the Senate blocks the proposal for a second time.

Greens housing spokesman Max Chandler-Mather asked the library to find out how much the average renter would have saved if rents had been frozen 12 months ago.

He further asked what the estimated average cost to lease a house in each capital city would be next year, based on a central bank projection that rents could rise by close to 10 per cent.

Using census and consumer price index data, the library estimated an average saving per occupied dwelling across the country of $1427 in 2022-2023 and $2261 in 2023/2024.

Collectively, roughly two million renting households could have saved $3.1 billion in 2022/23 and $4.9 billion in 2023/24, it found.

“These aren’t just numbers, a two year saving of $3688 per household is food on the table, a desperately needed trip to the dentist or it’s the electricity bills for two years,” Mr Chandler-Mather said.

“The prime minister has a historic opportunity to save the one-third of this country who rent.”

Mr Albanese has previously said a rent freeze was outside the Commonwealth’s jurisdiction because it was a state government responsibility.

But the Greens argue the prime minister could reach an agreement with the states via the national cabinet as he did last year to address soaring energy prices.

Acting leader Mehreen Faruqi said the prime minister had boasted about getting the state leaders to sign on to a new public holiday if the Matildas won the World Cup and could similarly use his national cabinet influence on housing.

“The prime minister absolutely has the power and the jurisdiction to be able to co-ordinate with states and territories to then implement rent freezes and rent caps,” she told ABC News.

Liberal frontbencher Dan Tehan said the rental plan from the Greens was going to make the shortage of apartments available for rent worse.

“What the government won’t discuss is why they don’t have a plan to deal with the 1.5 million people who are heading our way over the next five years,” he told reporters.

“That’s what’s going to put increased pressure on housing, on rates, on congestion, on health and also on the natural environment, and that needs to be part of this conversation.”

National cabinet is set to meet next Wednesday and housing affordability is expected to be a main topic of discussion.

Independent Victorian senator Lidia Thorpe is also pushing the government to amend its housing fund plan to allocate 10 per cent of new housing supply to Indigenous people.

Senator Thorpe is also calling for a standalone Indigenous housing and homelessness plan.