The fate of tens of thousands of social and affordable houses is on the line as the government tries to secure parliamentary support for its signature investment fund.

Laws to set up Labor's housing fund have stalled in the Senate with the Greens, who hold the balance of power, withholding support in the hopes of a larger package and a rent freeze.

But the government will seek to prioritise the legislation this week in the hopes of pushing it through the upper house - something the Greens have warned against.

The investment fund will leverage $10 billion and use the interest, up to $500 million a year, to roll out 30,000 new social and affordable rental homes across Australia over five years.

Housing Minister Julie Collins is imploring the Greens not to waste the opportunity.

"Senators can't say they support more social and affordable housing but oppose this fund," she told AAP in a statement.

"We know how urgently these homes are needed. Australians who need these homes will be watching closely."

Negotiations continue and when the legislation will be brought to a vote in the Senate is yet to be decided.

The Greens party room on Tuesday remained against the bill - including with the Lambie Network concessions - without further amendments.

A further round of negotiations between the government and minor party are slated for later in the week as they continue to push for a minimum guaranteed spend from the fund among other concessions.

Two Jacqui Lambie Network senators have signed onto the bill after receiving a guarantee that each state and territory will receive a minimum of 1200 homes.

The coalition remains opposed to the fund, saying the amount borrowed will push up interest rates and drive inflation.

"Increased borrowing in this legislation will only add to the inflationary impact and pressures that are on our economy and they inevitably lead to ever higher interest rates," Liberal frontbencher Anne Ruston told the Senate.

She said the government needed to do more heavy lifting instead of leaving it to the central bank to curb inflation through interest rate hikes.

"What is the Albanese government's answer to the pleas from the Reserve Bank to borrow less and spend less? It's to set up a fund with $10 billion worth of borrowings."

Senior minister Penny Wong chastised the Greens and the coalition for not supporting the fund, branding it a political stunt that blocked investment in affordable housing.

"It's so cynical to pretend you care about people who are struggling with rent, struggling with homelessness," she said.

The Greens are calling on the government to directly invest $5 billion into housing, saying it will lead to more than 100,000 more affordable homes alongside state and territory contributions.

Senator Mehreen Faruqi said the government could then maintain control of the homes and reinvest the rent it receives over the next decade.

"The big risks associated with the fund are not matched by the rewards," she added.

"Even if the fund were to make a big return, spending on housing is capped. There is no floor on spending, literally nothing could be invested in social and affordable housing in a given year."

If the bill remains deadlocked between the two parliamentary chambers, there is potential for it to be used as a double-dissolution election trigger.