Ulster Bank have said they will be dealing with the backlog for the rest of this week.
This is despite the bank previously saying that the payments problems would be sorted by Monday.
The technical errors, according to RBS, have now been fixed.
But, it has left Ulster Bank with a huge backlog of business to deal with which they say is taking longer than expected to sort through.
On Sunday, Ulster Bank issued a statement stating that they had "encountered a significant number of minor issues which require manual intervention."
The bank admitted that the scale of the backlog is "unprecedented."
It has already promised that any charges incurred as a result of the errors will be refund in full.
Chris Sullivan is Chief Executive of the UK Corporate Banking Division.
He told UTV the problem will be rectified at different times for customers depending on the banking service they use.
"I would say by the end of the week, we're confident we will be substantially through the problem.
"As each day goes by we will catch a day or more of the transactions that have occurred, but as you can imagine this is quite a broad group-wide, complex problem which means we've got to deal with the days that we have missed.
"We've got to bring those back into the system and we've got to deal with the stats [statistics] that's going through currently and make sure people are in a position to run their businesses and do their daily business as well."
Meanwhile, branches are opened until 6pm on Monday in around 80 branches throughout Ireland, it is believed 28 of those are based in Northern Ireland.
Antoinette McKeown, CEO of the Consumer Council, is highly critical of Ulster Bank's handling of the situation.
Despite the Consumer Council’s best efforts Ulster Bank still continue to say that 80 branches across Ireland are open until 6pm this evening. 28 branches are open in Northern Ireland.
Antoinette McKeown, Consumer Council
"They have been very slow to come out with information, when they did it was confusing, it continues to be misleading," she said.
"Why is Ulster Bank continuing to give information to the island of Ireland when they should be saying 28 branches, that's less than a third which is not good enough, are open until 6pm this evening," she continued.
"The Consumer Council are saying, particularly for people working full time, we want to see branches open until 7pm this evening and every evening this week until the situation is fully resolved."
Northern Ireland Independent Retail Trade Association (NIIRTA) has also expressed concern at the ongoing delays.
The association is concerned about the knock-on effect the disruption will have on salaries and direct debits due to be paid at the end of the month.
Glyn Roberts, NIIRTA Chief Executive, said: "We hope that Ulster Bank will redouble their efforts to ensure an early resolution of this problem.
"It is also crucial that Ulster Bank and all other local banks learn the lessons from this problem and ensure that appropriate back up systems are in place so that never again businesses, employees and consumers are put in this situation."
Irish Minister for European Affairs Lucinda Creighton says the government is extremely concerned with the bank's delay in resolving the problem.
"There's obviously a chain here in terms of payments and in terms of availability of cash for business and for families and people as we know are under extreme pressure at the moment," she said.
"People cannot afford the luxury of delaying receipt of salaries and so on. Ulster Bank has to sort this out as soon as possible."
Jill Kirby, Personal Finance Correspondent with the Sunday Times says the problem has been a "disaster" for consumers.
Ulster Bank telephone: 0800 231 232
"I think the biggest difficulty with a lot of people is they don't know what has gone through and what hasn't gone through because even some of the ATM machines have been closed. From the consumer's point of view it has been a bit of a disaster, especially perhaps for people who are going on holidays or who have been on holidays."