"It is very distressing for Ulster Bank customers to discover that money has gone missing from their bank account or that they may have had debit card transactions declined", said Mr McGrath.
It has previously pledged that no customers will be left out of pocket, and had made emergency cash available for affected customers.
Ulster Bank have promised that they're investigating the issue and will have it solved as soon as possible.
Hundreds of complaints from customers in the Republic of Ireland have been lodged, however, the bank claims nobody in Northern Ireland has been affected.
He is now urging the Oireachtas Finance Committee to call in the bank's officials without delay.
Ulster Bank customers who are incorrectly overdrawn are being advised that emergency cash is available. However, some customers have said they are still experiencing issues.
The bank has been accused of failing to invest in its payments systems. The computer failure affected the entire Royal Bank of Scotland (RBS) group, but Ulster Bank took longest to resolve the issue.
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The IT failure resulted in a €5 million fine from the Central Bank of Ireland at the time.
Ten weeks after the initial problem, the bank was still warning some customers that their statements might not be correct.
"I have just had my card declined".
It also insisted that no customers will be left out of pocket. They are asking affected customers to call 1850 424 365 (from overseas 00353 1 8047475) minicom - 0800 015 4422.
The problem has been going on since the start of the business week on Monday and Ulster Bank has launched an urgent investigation into the matter.
Some of the bank's customers have reported that their salaries have disappeared from their accounts, and that direct debits have not been paid.
The bank added that it is "working hard" to fix the issue and apologised for any inconvenience.