The Commonwealth Bank insists customers will not be charged overdraw fees on their accounts if they come forward with any money that is not theirs.
CBA spokesperson Steve Batten told ninemsn Finance that the bank was still “assessing” the situation and would be looking at recouping any lost funds.
"Every transaction regardless of an ATM will be captured, we are certainly aware of who took what," he said.
He refused to speculate on how much money was overdrawn from accounts and by how many people, but said that it could be around two days before this was known.
"It's a process and we are hoping that customers will do the right thing," he said.
"The vast majority of people have transacted normally and different customers will have different situations."
Yesterday a rogue computer was blamed for the chaos in the CBA system yesterday, which disabled EFTPOS and internet and phone banking and allowing ATM users to overdraw their accounts.
Police and security guards were called to control customers who rushed to Commonwealth Bank ATMs after they started dispensing free money, The Australian reported.
The bank said the problem started with "an issue overnight when conducting routine database maintenance" which got worse throughout the day.
Customers who refuse to give back cash they received by mistake from the malfunctioning ATMs nationwide could face up to 10 years' jail, police warn.
Users were allowed to overdraw up to $1000 from more than 40 malfunctioning ATMs across the country, but the bank says they will have to give the money back.
Col Dyson from the NSW Police fraud squad said customers who deliberately overdrew their accounts could be tracked using data from the ATMs, bank records and surveillance cameras.
"People should realise that even though an ATM has dispensed cash, they are not entitled to that money and are committing a criminal offence if they keep it," Detective Superintendent Dyson said
"They are putting themselves in major jeopardy as far as a very major criminal offence is concerned."
Superintendent Dyson said customers who overdrew their accounts had left a "fairly decent trail of evidence" and could expect to be contacted by police or the bank.
The Commonwealth Bank has now fixed its internet, phone and mobile banking systems.
Batten said that the majority of malfunctioning ATMs were in Sydney. CBA has more than 4000 ATMs in Australia, more than any other bank.