The Greens want a government-owned People's Bank to offer cheap mortgages to force competition in the "lazy" banking sector.
The Greens want a "People's Bank" to give Australians low-cost mortgages, while also stripping back negative gearing to make houses cheaper.
But Labor says the Greens' plan would flood more money into the housing market and push prices up.
Greens leader Richard Di Natale announced plans for the Reserve Bank to set interest rates and offer no-frills loans and banking.
"In the face of ongoing misconduct and price gouging, it's time for government to step in and ensure that there is a low-cost banking service, backed directly by the RBA, which is focused on the everyday savings and mortgage needs of customers," Senator Di Natale told the National Press Club on Wednesday.
"It will help turn around the recent decline in home ownership rates. It will also help stem the flow of lazy profits to the banks and inject some real competition into the banking sector."
Labor leader Bill Shorten said the plan was a "thought bubble" that needed more homework.
"The real answer here isn't to put more cheap cash into the market, which will actually just boost the cost of housing," Mr Shorten told reporters in Melbourne.
"What we should do is tackle negative gearing, and I think that's the better reform."
The Greens have already announced plans to cut back negative gearing, which Labor has since also adopted.
"If you are not competing with (negatively-geared) speculators and investors, you have downward pressure on the other side," Senator Di Natale said.
He said Australia is one of the few countries that makes it easier for wealthy people to buy second, third and fourth properties.
The plan reinforced the need for more competition to the big banks, and it called for changes to allow mutual banking providers to grow faster, credit union CUA said.
Senator Di Natale also announced plans for a universal basic income, as patterns of work change dramatically.
"People starting a job and being in that job for the next few decades, those days are almost over," he said.
"Our current social security system is outdated. It can't properly support those experiencing underemployment, insecure work and uncertain hours."
Mr Shorten said Labor believes in providing pensions to people who need them, but a universal income was "a bridge too far".
The Greens are also exploring plans for a government-owned energy retailer offering cheaper power bills in a re-regulated energy market.