Ulster Bank has confirmed that no customer, including those of other banks, will be left out of pocket as a result of the technical problems at the bank.
The bank said it continued to work around the clock to clear the backlog of payments.
Earlier, the Royal Bank of Scotland, which owns Ulster Bank, said it was confident it can restore a full service for customers for the start of next week.
Payments into and out of Ulster Bank accounts have been disrupted since Wednesday, with the bank blaming technical issues for the problems.
After the issue first arose Ulster Bank said the backlog of payments would be cleared by yesterday, however, it later revised that saying the number of payments that needed to be processed was unprecedented.
The bank has been facilitating customers who call into branches with payslips by giving them cash.
Many branches opened extended hours over the weekend.
However, this week presents an extra challenge as many monthly salaries will have to be processed.
Social welfare payments going into Ulster Bank accounts may also be hit.
The Central Bank's Director of Consumer Protection, Bernard Sheridan, said yesterday that he expected Ulster Bank to stick to commitments to resolve its technical problems by the end of the week.
Mr Sheridan said the Central Bank had been dealing with Ulster Bank at the highest level.
Ulster Bank says customers who are unable to get to their local branch through the usual methods can call their branch or 1800-205100 for assistance.