Debate has stalled on the government's $10 billion Housing Australia Future Fund after the Greens deferred the bill, arguing not enough was being done to protect renters.
The $10 billion fund would build 30,000 new social and affordable homes in its first five years using profits from the fund.
But Mr Chandler-Mather, who is also the Greens' housing spokesman, said more action was needed to tackle rental stress.
"What's disappointing is a lot of this has gotten quite personal, and devolved into these sorts of personal attacks," he told Sky News on Sunday.
"The government's doing that because they want to distract from the fact that they've put forward this Housing Australia Future Fund, but it's not as if it's even good, it will see the housing crisis get worse."
Debate on the fund has been deferred until October, to allow for state and territory leaders to discuss rental reform at the next national cabinet meeting.
The bill was deferred despite the government putting in an extra $2 billion of direct spending on social housing that would be allocated to states and territories.
Mr Chandler-Mather said more action was possible from the government, following a $19 billion surplus being reported for the past financial year, which was above previous forecasts.
"We've said we'd like $2.5 billion a year invested in public and affordable housing, we think that's modest given that (the government's) own expert bodies say we need $15 billion a year of investment," he said.
"It's not the perfect being the enemy of the good, we just want to at least tackle that side of the crisis."
The Greens have called for a cap on rent increases as part of the reforms.
"We know other jurisdictions around the world have cap rents at between two and three per cent every year," he said.
"Ideally, what we'd like to see is a freeze on rent increases temporarily. We know that it worked in Victoria during the pandemic, where rents actually went backwards during that period, and what it does is allow for renters to get back on their feet."
Education Minister Jason Clare said the Greens were standing in the way of support.
"If the Greens are serious here about making a positive contribution to put a roof over the head of more Aussies who need it, stop with the politics and play a helpful role here," he told Sky News.
"They don't think it's perfect, but it will help, and don't stand in the way of a program that will help to build more homes for people who need it."
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