Former Liberal minister Andrew Robb pressed the Turnbull government to hold a royal commission into the banks but one with a narrower scope to stymie the Labor Party's assault on the major banks, cabinet sources say.

A source familiar with the event has confirmed details reported by the Financial Review, saying that Mr Robb, a former trade minster in the Turnbull and Abbott governments, used a private gathering convened by the cabinet minister Kelly O'Dwyer last week to push for an inquiry so that it might close the issue.

"He said Labor wouldn't give up on their political demands and maybe we should consider holding a narrow one [inquiry] to say we have done it," the source told Fairfax Media.

But Ms O'Dwyer, Minister for Revenue and Financial Services, pushed back according to sources, questioning whether the government, which is elected to govern in the national interest, would be expected to cave into all the "wild demands" oppositions propose.