Crossbench MPs are stepping up the pressure for the Government to rein in the banks, throwing their support behind a Greens bill before the Parliament.

The Government has promised to announce a package to encourage more competition within the sector before the end of the year, and the Opposition has also introduced a bill aimed at cracking down on price signalling.

But crossbench MPs say neither major party is doing enough and have pledged broad support for the bill put forward by the Greens.

The Greens bill wants to abolish $2 ATM fees, require banks to offer a basic fee-free account, and restrain banks from lifting mortgage interest rates too high.

Greens MP Adam Bandt says while other crossbench MPs may want to introduce amendments, he has their support for his bill.

"For any reform package to get passed through the House of Representatives it is going to need the support of the crossbenches," he said.

"One thing is absolutely clear, and Labor and [the] Liberals should reflect on over summer, that if they want either of their packages to go through they're going to need to talk to us."

Western Australian Nationals MP Tony Crook, who sits on the crossbench, says the major parties need to step up action against the banks.

"There's a real opportunity over the summer break for both the Government and Opposition to put forward some serious amendments along with the Greens bill," he said.

Independent MP Andrew Wilkie says the Government has been "flat-footed" on the issue.

"I for one will back any package of sensible banking reform from any political party if it will rein the banks in," he said.

Independents Bob Katter, Rob Oakeshott and Tony Windsor are also supporting Mr Bandt's bill, which is not due to be voted on until next year.