“I want to negotiate in good faith,” she said,adding she was open to discussions about getting the bills back before the Senate later this week.

“There are vulnerable people relying on this bill passing,so we can get returns and homes on the ground as quickly as possible.”

After lengthy negotiations,the Greens agreed on Monday to support the government’s safeguard mechanism bill witha new hard cap on emissions from big polluters.

In its party room meeting on Tuesday morning,the Greens agreed to push the National Reconstruction Fund and the safeguard mechanism bills through the Senate on Wednesday and Thursday,but not the housing bills.

The housing fund is meant to provide $500 million a year in returns to get 30,000 social and affordable homes built over the next five years,and will also provide $200 million to repair housing in remote Indigenous communities,$100 million for crisis accommodation for women and children escaping domestic violence,and $30 million for housing for veterans.

This is the last parliamentary sitting week before the May budget,and the government had hoped its housing bills would be passed this week so the $10 billion fund could be set up soon and potentially start providing returns by the end of the year.

On Tuesday afternoon,Collins urged the Senate to pass the bills,saying the main affordable housing peak bodies including the Community Housing Industry Association and National Shelter wanted the policy passed as soon as possible to help Australians struggling with rising interest rates and rents.

“[That] is why we moved immediately last year to unlock $575 million to get more social and affordable housing on the ground quickly,” she said in question time.

Collins said crossbench MPs should talk to their senators to get the housing policy passed.

“I would say to them,what you are saying is no to actually getting homes on the ground or people that need it most,” she said.

Chandler-Mather said other groups,including construction union the CFMEU,Anglicare Australia and Master Builders Australia wanted the government to do more on housing.

“What we want to see is a national two-year freeze on rent increases to give renters real relief. We want at least $5 billion of investment in public,community and affordable housing. And we want a billion dollars for First Nations’ housing,” he said.

“That is eminently reasonable in the context where the government has just found$368 billion for the nuclear attack submarines.”

Earlier on Tuesday,Collins said a national rent freeze was not something the government had power over.

“Constitutionally,that sits with states and territories. It’s not something that we have purview over. The states and territories have all the levers available to them,” she said on ABCNews Radio.

“What I can do is obviously ... meet regularly with states and territory ministers and talk about a whole range of issues. What I can do with them is negotiate another Housing and Homelessness Agreement from 1 July 2024.”

But Chandler-Mather said there were plenty of precedents for the federal government to negotiate with the states and territories for a national approach to an issue,including an agreement reached last year on energy price caps.

“What we’ve said is that they should,either via national cabinet or the next national housing and homelessness agreement,say it’s a condition for that agreement for states to introduce rent caps,” he said.

CFMEU national secretary Zack Smith said the federal government’s plan to spend $500 million a year on social and affordable housing was “just not enough”.

“We need to see a serious level of funding to deal with this issue,and we need to be prepared to tackle this problem seriously,and not throw a bucket of water on a bushfire,” he said at the rally.

Smith said the union was part of the broader Labor movement,but social and affordable housing were incredibly important issues.

“We will be prepared to campaign to see more funding for social housing and to see better safeguards on how that money is spent,” he said.

Cut through the noise of federal politics with news,views and expert analysis from Jacqueline Maley. Subscribers can sign up to our weeklyInside Politics newsletter here.