Westpac chairman Lindsay Maxsted has warned it was "very dangerous" to send a signal to global markets that there could be problems within the banking system that warranted a royal commission.

Mr Maxsted was called to a late-afternoon meetings with Treasurer Scott Morrison, who also arranged meetings with three other bank chairs, as the Treasurer looked to head off a backbench push for a royal commission.

"What messages does that send to the rest of the world, who by the way think we have got one of the safest and most secure and stable banking systems in the world?," Mr Maxsted said of a royal commission.

"There's some problem there? They need a royal commission? What's that telling me that I don't know about? Very dangerous stuff," he said at a business lunch in Sydney.

Treasurer Scott Morrison: "For some years now I've been talking to the banks about resolving some legacy cases where people have had issues." Alex Ellinghausen

On Thursday, Mr Morrison said he talked "to the banks about resolving some legacy cases where people have had issues".

"These cases have been raised in various forums and I've been impressing upon them for some time now the need for those cases to be resolved."

Prime Minister Malcolm Turnbull has repeatedly denied any need for a royal commission after a series of scandals in the banking sector, but Nationals senator Barry O'Sullivan believes he has the numbers go ahead without cabinet approval.

The move would require the support of two Coalition MPs to cross the floor in the House of Representatives to suspend standing orders, the first step in establishing an equally powerful parliamentary commission of inquiry, which could destabilise the Turnbull government.

The country's biggest banks including Westpac, ANZ, National Australia Bank and the Commonwealth Bank have reportedly been bolstering their legal teams. Arsineh Houspian

"If both houses of the parliament think this is a good thing to do and that is the decision, I think the Prime Minister has to sort of sit up and take note and support the parliamentary decision," Senator O'Sullivan said on Monday.

His office has become a de-facto complaints centre for aggrieved customers following a catalogue of scandals, including the financial planning arm of the Commonwealth Bank and its CommInsure life insurance branch.

Foreign Minister Julie Bishop has called for a formal investigation into the leak on Thursday, but Treasurer Scott Morrison would not be drawn.

Commonwealth Bank chief executive Ian Narev pushed back against Senator O'Sullivan's calls by arguing lenders were already grappling with a suite of policy changes, tougher regulation, and court cases.

Management and boards of banks were actively responding to community concerns, he said.

I think it's incredibly important these issues are resolved and I'm sure the Prime Minister has this well in hand. Scott Morrison

"If people want more than that, they are saying the justice system has failed, the political system has failed, the regulatory system has failed, and bank management and bank boards have all failed," Mr Narev said.