Labor will use the biggest boost to cheap homes in a decade to try to wrest control of the housing agenda as it faces defeat on key policies to alleviate Australia’s shortage of affordable properties.

Prime Minister Anthony Albanese has revealed his government will fund nearly 14,000 new homes through the first cash injection from the $10 billion Housing Australia Future Fund, which invests in the stock market to generate an estimated $500 million a year.

But the Greens have accused Labor of “self-sabotage” on two bills – one helping pay people’s deposits and the other encouraging the building of long-term rentals – with the minor party’s housing spokesman, Max Chandler-Mather, claiming it is unwilling to negotiate with him.

Senior government sources, speaking anonymously to be candid, said Labor would obviously prefer the bills to pass but was resigned to Greens and Coalition opposition.

If the bills were rejected in the Senate, which will debate the help-to-buy scheme this week, Labor would be able to claim at the election that the Greens were blocking solutions and the government needed a second term to fix the problem, the sources said.

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The opposition and the Greens have put expensive properties and rents at the centre of their attacks on the Albanese government’s management of living standards. For months, they have pressured Labor to start using the $10 billion fund approved by the parliament a year ago. Labor may expand the $10 billion scheme as it searches for new policies.

The initial outlay will create up to 4200 social houses, built by non-profits for low-income people, and nearly 10,000 affordable homes that are more expensive but still designed for lower and middle-income households.

“I grew up in social housing – I know how important a roof over your head is and the opportunities it creates,” Albanese said in a statement.