Ulster Bank has said due to the length of time it is taking to work through a payments backlog it will not be fully operational on Monday.
The backlog was caused by a software problem last week.
Twenty Ulster Bank branches were opened across Ireland from 10:00 BST until 13:00 BST on Sunday - eight of them in Northern Ireland.
The bank said "thousands of employees are working around the clock" to clear the backlog.
"We have extra staff in our call centres to deal with customer queries," the bank said.
"Yesterday, we answered over 6,600 customer telephony queries, with all of these answered within 20 seconds. We have had 95% availability on our ATM network throughout the weekend.
"Yesterday we dealt with over 9,000 customers in our 60 Saturday opening branches."
The bank's branches will be open until 18:00 BST on Monday.
"We continue to apologise unreservedly to customers who are experiencing difficulties as a result of this issue," the spokesperson said.
The technical fault has disrupted payments into and out of thousands of customer accounts since Wednesday.
On Saturday, Antoinette McKeown from the Consumer Council said they were concerned about the lack of response from the bank.
She said the information it had given 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.