A $10 billion commitment to support the construction of 30,000 affordable homes over the next five years is at risk of defeat in the Senate.

The Greens are weighing up their position on Labor’s election commitment for a Housing Australia Future Fund to build thousands of new social and affordable homes.

Prime Minister Anthony Albanese said the rhetoric surrounding the housing fund was “rather strange”.

“If people think that it’s a great idea to say that they support more investment in social housing, but not back a $10 billion fund that will build more social and affordable housing, then good luck having that argument,” he told reporters in Canberra.

With the bill listed for debate in the Senate, independent senator Jacqui Lambie said discussions with the government would continue over the coming days.

“We’re concerned about the set-up and the way they have done their costs,” she told Seven’s Sunrise program.

“This is also going to come down to once again the Greens, and whether or not they support it.”

The government needs the Greens and two Senate crossbenchers for its legislation to pass the upper house.

The Greens are pushing for rents to be frozen for two years and a million new homes built to address the housing crisis.

Greens senator Mehreen Faruqi said the government had already set a precedent by intervening in the energy market and capping prices.

“More people than ever are living in cars, caravans, and tents. More and more people are struggling to pay rent,” she said.

“Will the government finally do the same thing they did for energy caps and coordinate a national freeze on rent increases and coordinate national tenancy standards?”

Cabinet minister Don Farrell said the proposed fund would help address rent spikes by increasing supply.

“The answer to rental stress is a sustained boost in the supply of homes to rent, and a substantial investment in new social and affordable houses,” he told parliament.

“That’s what this government is aiming to do.”

ACT independent senator David ­Pocock has also reaffirmed he won’t support the bill in its current form.

Peak body National Shelter has described the bill as “the most critical housing legislation to be brought forward for the past 10 years”.

– AAP