Ulster Bank has said it is unlikely the backlog of payments caused by technical problems will be cleared by Monday.
The bank has said that it is "working around the clock" to resolve the problems and is opening branches on Sunday for the first time in a bid to help affected customers.
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.