National Australia Bank's new chief executive Ross McEwan says the bank must lift its game and has told senior executives to "fear me" if they have deliberately ripped off customers, as the lender tries to regain public trust after a run of scandals.

With some investors keen to see Mr McEwan ramp up cost-cutting against a soft profit backdrop, the NAB chief also signalled he would have a "very strong" look at the bank's costs, in order to deliver shareholder returns.

NAB chief executive Ross McEwan. Credit:Brendon Thorne

In his first detailed public comments since starting as CEO earlier this month, Mr McEwan on Wednesday told shareholders at an annual general meeting that NAB needed to get the "get the basics right,” which included a sharper focus on customers.

A day after the corporate cop launched legal action accusing NAB of more than 12,000 breaches over the "fees for no service" scandal, Mr McEwan said some problems it faced were "not acceptable."