Chief Executive of Royal Bank of Scotland Stephen Hester met with the Central Bank's Head of Financial Regulation today.
The meeting with Matthew Elderfield took place at the Central Bank.
It is understood authorities here have expressed dissatisfaction with Ulster Bank's communications of the technical chaos.
It is also understood the Central Bank believes that Ulster Bank was slow to react to its technical problems.
Earlier, Ulster Bank said it could not predict when normal service would resume for its customers, two weeks after its technical breakdown affected thousands.
It said that it could not commit to any timescale in terms of clearing the backlog in unprocessed payments.
The bank had earlier pledged that the backlog of payments would be cleared by the beginning of this week.
A spokesperson said it cannot quantify how many transactions remain in the system, but it is a "significant number".
In a statement this morning, the bank said there may be “some bumps along the road” as it sorts through its transaction backlog.
It said: “We target that customers should see their balances updating during the coming week.
“However, normal service will take some further time as our experience from dealing with the same issues in the UK suggests that there may be bumps along the road.”
The bank said it would carry out a full investigation, with independent experts, once the issues have been resolved.
Ulster Bank's parent group, Royal Bank of Scotland, has apologised to its Irish customers, whose problems have lasted far longer than those at NatWest.
RBS said this was due to the sequencing of the three banks' systems and did not reflect the priority attached to Ulster Bank customers.
Mr Hester said: "I want to apologise to our Ulster Bank customers for the significant inconvenience caused by these technology problems.
"I recognise that being sorry is not enough; we believe we have fixed the initial problem and are now making inroads in catching up with the knock-on effects to our customers in Ulster Bank.”
About 50 Ulster Bank branches will extend their hours of business again this week to assist customers.
The Department of Social Protection has said it has an additional 48,000 monthly payments due to be paid to Ulster Bank customers tomorrow. This is on top of the usual weekly payments.
The Department said it has been liaising with Ulster Bank and the bank has said that it is preparing for the possibility of additional footfall.
Meanwhile, the Central Bank has been called before an Oireachtas Finance Committee this week to answer questions about its regulation of Ulster Bank.