Treasurer Scott Morrison has turned up the political pressure on the Commonwealth Bank, saying the lender has had an "epic fail" and citing "very troubling" issues of culture and governance.

After the explosive allegations that it breached anti-money laundering laws overshadowed CBA's $9.9 billion annual profit on Wednesday, Mr Morrison criticised the bank over the affair but gave no further clues about how the government may respond - if at all.

"First of all, I think it is an epic fail and I think it's incredibly serious, and at the end of the day, it's in the first instance that the Commonwealth Bank – and particularly their board – [has] to assure the public about their confidence in that bank," Mr Morrison said on ABC Radio's AM program on Thursday.

Mr Morrison met with CBA chairman Catherine Livingstone on Tuesday, after financial intelligence agency Austrac last week alleged the bank had failed to report to authorities thousands of large transactions in its ATM network, and that criminal gangs had laundered millions through the bank.