Ulster Bank has confirmed its customers will be able to access the funds in their bank accounts this weekend.
Sixty branches of the bank will open tomorrow, and possibly Sunday, to help resolve the backlog created by technical problems.
The company said a software glitch meant automatic salary and social welfare payments have not been processed, and it has estimated that at least 100,000 customers have been affected.
Social Protection Minister Joan Burton earlier hit out at the bank, calling on them to open over the weekend if it is not fixed before then.
Chief Operating Officer of the Ulster Bank Group Ellvena Graham apologised for the problems.
"Our focus over the last couple of days has simply been on our customers," Graham said.
"We are now in a much better position to communicate with our customers and we're keeping our branches open late this evening.
"We're keeping a number of branches open until 3pm tomorrow to try and help as many customers as we can."