Commonwealth Bank says a string of failures in its automated reporting system may be only one breach of the law, which would mean any fine facing the bank over allegations it broke anti-money laundering laws would be drastically lower than speculated.

It came as chief executive Ian Narev said the board of directors would take "very serious account" of the latest scandal to hit the bank when it was deciding on executive bonuses for the year, in board meetings on Monday.

The country's largest bank is embroiled in a fresh scandal after the financial intelligence agency, Austrac, last week alleged it failed to inform authorities about suspect cash deposits at its ATMs.

Some of the transactions were made by criminal gangs laundering millions of dollars, and even some possible terrorists, Austrac alleges.