Ulster Bank: Sir Mervyn King calls for RBS inquiry
The governor of the Bank of England has called for a detailed inquiry to be carried out, into what went wrong with computer systems at the RBS group.
Customers at Royal Bank of Scotland (RBS), which owns Ulster Bank, and NatWest were also affected.
Sir Mervyn King said the problems showed the importance of focusing on banking services.
Ulster Bank said about 30 of its branches would remain open late to process a backlog of transactions.
The bank said the scale of the backlog was "unprecedented" and warned it could be a week before operations return to normal.
At the weekend, Ulster Bank branches opened to deal with problems created by the failure.
Chris Sullivan, chief executive of corporate banking at RBS, said every effort was being made to ensure customers were not disadvantaged.
"We are putting all of our efforts into ensuring that nobody is out of pocket in this situation. We have a team working on all eventualities," he said.
"We are really sorry this has occurred. This is the last thing any bank would want. We are taking this really seriously."
The chief executive of the Citizens Advice Bureaux (CAB), Derek Alcorn, said he had spoken to the Ulster Bank and was assured that if customers brought proof of identity into the bank, they would receive their benefits or salary.
He said the CAB was available to help anyone having difficulties because of the bank failure.
About 27,000 social security agency customers have been affected by the problems.
Ulster Bank said extra staff had been drafted in to answer queries and resolve any financial worries customers may have had.
The bank has apologised again to customers affected.
It said thousands of employees were working around the clock to clear the backlog.
Customers can find answers to questions linked to the technical backlog, as well as details of the branches offering extended opening hours on the Ulster Bank website .