The Australian Transaction Reports and Analysis Centre (Austrac) said the banks' actions had left their services and the wider financial system vulnerable to potential abuse by criminals looking to launder the proceeds of crime or finance terrorism.
Barclays has undertaken to review all account transactions carried out since July 1st 2002 and will report any suspicious activity to Austrac. It will also have to submit information about any large fund transfers into or out of Australia.
Mega International has provided a similar guarantee to review transactions since January 2002, although the Australian daily noted that Austrac remains concerned that the bank may still in breach of Australian law.
Austrac chief executive Neil Jensen said: "During a period of global financial concerns we need to be even more vigilant, as a range of scams have commenced during this period."