Jobs Minister Richard Bruton is calling on Ulster Bank to suspend all charges on its customers' overdrafts until its technical problems have been completely fixed.
Mr Bruton's comments came after Ulster Bank announced earlier that the scale of the backlog of payments on its systems was unprecedented and might not be cleared until the end of this week.
The bank has been facilitating customers who call into branches with payslips and giving them cash.
This week presents a particular challenge, as many monthly salaries will have to be processed.
Minister Bruton told WLR that Ulster Bank customers should not be left out of pocket because of this computer glitch.
"I think the needs of customers have to be paramount...I think people have to be protected also in terms of charges that they might face because of this and the fear of downgrade of their credit," he said.
"I think the bank should be considering suspending charges for this period, until they sort out the service."