National Australia Bank has promised to compensate customers who suffered financial losses after a national outage that hit mobile banking, ATMs and eftpos for several hours.

Most services have now been restored after the outage, caused by a series of faults originating from a power failure, which left many NAB customers across Australia furious on Saturday.

NAB automatic teller machines were out of action for several hours on Saturday. Credit:AAP

"If there was a loss that was driven by the outage today then compensation will be provided to customers," NAB Business executive general manager Cindy Batchelor told reporters in Melbourne on Saturday afternoon.

"We'll work with each and every one of them to understand exactly what happened to that particular customer."