The top bosses of National Australia Bank - the parent company of the Bank of New Zealand - have resigned and say they are "deeply sorry" for failings by the bank.

The resignations come just days after a damning report on the finance sector was delivered in Australia in which the NAB was highly criticised.

Chief executive Andrew Thorburn and chairman Ken Henry both said they would leave the bank in a statement to the Australian stock exchange released yesterday late afternoon.

The announcement came three days after commissioner Kenneth Hayne delivered a highly critical report on the banking and financial services industry which recommends sweeping changes be made.

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In the statement, Thorburn said he had had a number of conversations with the chairman this week.

"I acknowledge that the bank has sustained damage as a result of its past practices and comments in the Royal Commission's final report about them.

Thorburn who has been NAB group CEO since 2014 when he moved from the top job at the BNZ, said he had always sought to act in the best interests of the bank and customers had acted with integrity.

"However, I recognise there is a desire for change."

Thorburn said he had offered to step down and the board had accepted.

"I have devoted myself to serve NAB and my hope and ambition is that bank can move forward and achieve its vision of being trusted by customers for exceptional service."

Thorburn will finish up at the end of the month with current NAB director Philip Chronican to take over as acting chief executive until a permanent appointment was made.

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Henry will retire from the board once a new permanent chief executive was appointed.

He said he and the board had recognised that change was necessary.

"The timing of my departure will minimise disruption for customers, employees and shareholders."

Henry said he was proud of what the bank had achieved and equally disappointed about what the Royal Commission has brought to light in areas where the bank had not met customer expectations.

"Andrew and I are deeply sorry for this."

"My decision is not made in reaction to any specific event, but more broadly looking at the bank's needs in coming months and years."

Henry said the board would bring on new non-executive directors this year to increase its diversity of thinking and establish a committee for customer outcomes.

Both Thorburn and Henry had been in the spotlight after commissioner Hayne wrote in his final report he was less confident the two leaders at NAB had learnt any lessons from the inquiry into the sector.

"More particularly, I was not persuaded that NAB is willing to accept the necessary responsibility for deciding, for itself, what is the right thing to do, and then having its staff act accordingly," he wrote.

"Overall, my fear — that there may be a wide gap between the public face NAB seeks to show and what it does in practice — remains."

- Additional reporting news.com.au.