Greens MP and banking spokesperson Adam Bandt has warned the banks against increasing rates following the RBA decision to keep rates on hold.

Mr Bandt says the banks would break their social contract with the Australian public and that he will move ahead with legislation to rein in the banks.

"If the ANZ or other banks hike their rates they risk breaking their social contract with the Australian people."

"The Treasurer should get behind the Greens' legislation for banks to provide mortgages that track RBA rates."

"The banks should no longer expect the Australian public and government to generously back them in a crisis unless they give something back."

"The IMF has said banks could pay a "too-big-to-fail" levy in return for deposit and funding guarantees, and we agree."