Bank of Ireland has warned customers that money withdrawn from their accounts while its online and app services were down will still be debited from their accounts.
It comes amid reports of some users being able to withdraw money beyond what they expect to be in their account.
An Garda Siochana said it was aware of an “unusual volume of activity” at some ATMs across the country.
It said it was also aware of issues relating to banking services on Tuesday.
In a statement to the PA news agency, a Bank of Ireland spokesman said: “We would like to remind customers that if they transfer or withdraw funds – including over their normal limits – this money will be debited from their account.
“While we are conscious customers may not be able to check their balance at this time, they should not withdraw or transfer funds if they are likely to become overdrawn.“
An Garda Siochana also said it would “remind people of their personal responsibility in carrying out their personal banking”.
A spokesman for banking technology firm Revolut told PA it was “looking into” claims that excess amounts of money had been transferred into customer’s accounts from Bank of Ireland.
Earlier, Bank of Ireland said it does not have an estimated time for when its mobile app and web service 365Online will be restored.
Upon opening the app, users are informed they are unable to connect while the website is also unavailable.
The bank has told customers that its technical team is working to rectify the difficulties as a “high priority”.
Customers reported having no access to their accounts for hours and being unable to transfer money for “important payments”.
Apologising to users, Bank of Ireland said: “We are aware that customers using our mobile app and 365Online are currently experiencing difficulties.
“We are working to fix this issue as quickly as possible and apologise for any inconvenience caused.”
The bank also acknowledged that some customers were having difficulties withdrawing cash from ATMs.
Shortly before 10pm on Tuesday, the bank added that it did not “have an ETA” for the restoration of services.
