Ulster Bank is to open branches on a Sunday for the first time, to help customers whose accounts have stopped working because of a technical fault.
Twenty branches will open across Ireland from 10:00 BST until 13:00 BST - eight of them in Northern Ireland.
On Saturday, the bank said it was unlikely the backlog of payments would be cleared by Monday.
The bank said that it was "working around the clock" to resolve the problems.
The technical fault has disrupted payments into and out of thousands of customer accounts since Thursday.
The bank acknowledged the problem was causing "unacceptable inconvenience".
"We continue to apologise for any difficulties (customers) are experiencing as a result," the bank said.
"We want to reassure customers that no one will be left permanently out of pocket as a result of this issue.
"We will have 20 Ulster Bank branches open tomorrow, Sunday 24th, from 10am to 1pm to deal with customers and we will continue to post regular updates on our website ."
Earlier, Antoinette McKeown from the Consumer Council said they were concerned about the lack of response from the bank.
She said the information that had come had been confusing.
"We understand and sympathise that systems do fail but we have been very disappointed with Ulster Bank's response," she said.
"They have been very, very slow to come out with information.
"When Ulster Bank did come out with information it was confusing, it was misleading.
"There has been a distinct lack of leadership presence from the Ulster Bank."
On Friday, Ulster Bank's Ellvena Graham explained that although the software problem was resolved on Wednesday, the bank is experiencing a two-day delay to its processes because of the size of the group.
Payroll and social welfare payments have been affected, however, she said customers can access their money by going into any Ulster Bank branch or contacting their call centre.