The Director of Consumer Protection at the Central Bank has said that it views the matters that have arisen in Ulster Bank extremely seriously.
The backlog of unprocessed transactions at Ulster Bank stems from a technical breakdown two weeks ago.
Customers are continuing to experience difficulties as payments fail to reach their accounts.
Addressing the Oireachtas Finance Committee, Bernard Sheridan said the breakdown was unprecedented and described the contingency planning of Ulster Bank and its parent group RBS as appalling.
Mr Sheridan said the bank’s approach to customer communications was at times exasperating.
"What happened was unacceptable, and remains so today." He said this view has been articulated to Ulster Bank and RBS.
Mr Sheridan said that the Central Bank would be insisting on a restitution plan for customers.
He said that the bank’s "first touch" on this issue had been extremely poor on the communications front with customers.
Mr Sheridan said the Central Bank had taken extensive steps to minimise the impact of the problem in terms of not disrupting the National Payment System.
However, Fianna Fáil’s Michael McGrath criticised the Central Bank for being too slow to react to the situation.
Ulster Bank said today the "significant delays" will continue until next week and the "vast majority of customers" will have a normal service by 16 July.
Meanwhile, The Irish Bank Officials Association has asked customers of Ulster Bank to resist the urge to use staff as an easy target.
The IBOA said that bank officials share the customers' sense of frustration but asked that the public direct their criticisms directly to bank's senior management.
Larry Broderick, General Secretary of the IBOA said that an effective contingency plan, and a standalone Ulster Bank IT system, needs to be put in place to prevent any repeat of this "catastrophic situation" in the future.
Ulster Bank CEO Jim Brown said: "We know customers are frustrated and they are right to be.
"Our efforts to fix this are paying off and over the last few days we have been able to gain a much clearer picture about when we expect all systems to be largely back to normal."
Mr Brown told RTÉ News that the bank is considering ways of compensating customers affected by the problem.
He said it would be looking at its options over the coming days and that no one would be left out of pocket.
Representatives of Ulster Bank are due before the committee tomorrow.
Elsewhere, Northern Ireland's finance minister said Ulster Bank has lost the confidence and trust of its customers.
Sammy Wilson said the bank needs to move quickly to restore faith.
MPs from Northern Ireland are meeting senior executives from RBS in London today.
SDLP MP Margaret Ritchie said the two weeks of disruption to accounts was unacceptable.
DUP MP Nigel Dodds said the parent company needs to deploy more resources and personnel to ensure Ulster Bank can deal with the level of crisis it now faces.
British Prime Minister David Cameron told the House of Commons that the crisis at Ulster Bank is "unacceptable" and that "lessons must be learnt" from the crisis.