The federal government has approved grants for the construction of thousands of social and rent-capped homes, the first to be supported by its $10 billion housing fund established one year ago.

Housing Minister Clare O'Neil said 185 housing projects had been green-lit in the first round of grants distributed through the Housing Australia Future Fund (HAFF), a move which would deliver a combined 13,700 homes.

That puts the government ahead of its target to build 40,000 homes in the fund's first five years of operation.

Ms O'Neil said the government was "back in the game of delivering social and affordable houses at scale, working with all levels of government and the community housing sector to deliver the biggest investment in social housing in over a decade".

The successful projects represent roughly one-quarter of the 673 applications submitted to government agency Housing Australia earlier this year.

The full set of applications, which spanned the government, community and private sectors, was for a total of more than 50,000 houses, but the amount the fund can spend each year is limited and tied to how much interest the fund has accrued. There is a minimum required spend of $500 million each year.

The grants last for 25 years and take the form of a regular "availability payment" in exchange for the housing remaining available for the full duration.

Of the approved homes, 4,220 will be social housing, where rent is set at a level affordable by those on low incomes. Another 9,522 will be "affordable" homes, capped at three-quarters of market rent.

A total of 1,267 are designated for women and children escaping family violence and older women at risk of homelessness.

Ms O'Neil said 40 per cent of the successful applicants would start construction this financial year.

"We want to reduce the stress of housing for Australians – the long waits on housing lists, the long queues for rentals, the out-of-reach deposit for first home buyers. We'll reduce these issues if we build more houses, and that's what these projects do," she said.

Housing Australia chief Nathan Dal Bon told a Senate estimates hearing in June that the completion dates would vary widely, with townhouses able to be finished in "a relatively short period of time" but apartments likely to take "years".

The government will list its Help To Buy shared equity housing scheme for debate in the Senate this week, where it is widely expected to fail.

The bill, which was approved by the House in February, would see the government co-purchase homes with up to 40,000 first homebuyers, modelled on similar schemes at the state and territory level and overseas.

The Coalition campaigned against the idea at the last election, saying homebuyers would not want the government to own part of their house.

Greens housing spokesperson Max Chandler-Mather has said the idea would "drive up house prices" but that he is willing to negotiate if the government considers negative gearing reform, a publicly owned property developer, more social housing funding, or rent caps and freezes co-ordinated with states and territories.

The Greens entered negotiations over the HAFF with a similar list of demands and ultimately agreed to pass it after Labor agreed to billions in additional social housing funding.

But there has been no sign of movement from either party for several months, and in a media release on Sunday the government appeared resigned to its failure, accusing the Coalitions and the Greens of "blocking" it.

Mr Chandler-Mather accused the government of refusing to engage in "good-faith negotiations".

"Labor has offered absolutely nothing … [They are] not negotiating, they haven't made a single counteroffer, and frankly we have lost patience," he said.