Launa Inman, a director since 2011, and Harrison Young, a board member since 2007, will both vacate their seats.

Inman was a member of the board's audit and remuneration committees while Young occupied a seat on the risk, audit and nominations panel. Both will leave in November.

The bank has been under pressure since the monitoring agency AUSTRAC filed a civil case against it in August for allegedly violating Australian anti-money laundering and counter-terrorism financing laws.

AUSTRAC claims that CBA contravened the laws more than 53,700 times and to a total value of more than $77 million. Any transaction over $10,000 is supposed to be reported within 10 days.

Meanwhile, other reports say the bank's alleged failure to monitor transactions will lead to action by US regulators.

Fairfax Media reported that the bank was already answering questions from a number of American bodies and it was only a matter of time before a formal probe was announced.

A Washington lawyer said the US financial intelligence unit FinCEN would already be involved through its understandings with AUSTRAC.

He said CBA had US branches and dealt in US dollars, both reasons why it would have to follow US anti-money laundering laws.

The civil case against CBA opened on Monday and the bank has been given time until 15 December to file its defence against the charges, after the presiding judge was told that it would not largely contest the main charges being levelled against it.