Galway Senator Lorraine Higgins has delivered a cross-party petition to Ulster Bank calling for an assurance that the bank will waive customer charges until next year.
The Labour Senator said the petition "should be an important wake up call to Ulster Bank".
Ms Higgins has previously accused the bank of cutting corners and of having a "fast buck" mentality.
Ulster Bank has said it is making steady progress in restoring normal services for customers who have been affected by the bank's payments backlog.
In its latest update, the bank said the majority of accounts now show updated balances.
However, some cheques, manual lodgements and payments have yet to be processed.
Ulster Bank expects that services will be fully operational by next Monday.
