Royal Bank of Scotland CEO Stephen Hester met with the Central Bank's head of financial regulation Matthew Elderfield today.
The meeting took place in the Central Bank in Dame Street. It is understood authorities in Ireland 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.
Meanwhile, Ulster Bank has said it can not predict when normal service will resume for its customers.
It also said it can not commit to any timescale in terms of clearing the backlog in unprocessed payments.
Ulster's parent company, the Royal Bank of Scotland, has today apologised to its Irish customers.
Three weeks after Ulster's technical breakdown, there is still no firm end in sight as the bank admits it does not know when accounts will be fully back to normal.
The bank can not also say how many transactions remain to be processed, although it is a significant number.
Ulster's Bank's problems have far outlasted those of NatWest in Britain which were due to the same software glitch.
RBS said on an average day it processes around 20 million transactions. These are done in batches through an automated system. The bank said that clearing the backlog had to be done in sequence, in order for the automated system to recommence.
RBS said the reason why NatWest and RBS customers in the UK had their problems resolved before those in Ireland, was that Ulster Bank follows the other two banks in the sequence for processing transactions.
It said this is because of the way the technology was set up when the three banks were integrated, and is not a reflection of the priority it attaches to Ulster Bank customers.
RBS group chief executive Stephen Hester said he recognises that sorry is not enough.
Read the RBS statement in full here
He said Ireland is important to them, pointing out that they had maintained a full banking service in Ireland through the financial crisis, as others left the market here.
Meanwhile, the Central Bank has been called before the Oireachtas Finance Committee this week to answer questions about its regulation of Ulster Bank.
As the issue continues, another 48,000 monthly social welfare payments - including childrens' allowance - are due to be paid into Ulster Bank accounts tomorrow.
