A spokesman for the bank said they were "working flat out to get these payments updated for our customers no later than Saturday".
Its parent company RBS said about 600,000 payments were affected.
It said it had now identified and fixed the underlying problem.
Ulster Bank said concerned customers should "come into a branch or get in touch with our call centres".
"We will ensure no customers are left out of pocket as a result of this issue," a spokesman said.
In 2012, the RBS group was hit by a major IT meltdown that led to a large fine.
RBS, NatWest and Ulster Bank customers were affected in June 2012 after problems with a software upgrade. On that occasion, the IT failure affected more than 6.5 million customers in the UK over several weeks.
The banking group said it had invested hundreds of millions of pounds to improve its computer systems since then.
Ulster Bank is working to restore payments and direct debits that were delayed by a computer glitch involving the RBS group of banks.