Customers have taken to social media to complain about the impact the IT failure is having on them.
One person said they had to "put back my shopping because of it", while another said they were "waiting to go shopping" but couldn't transfer money to do so.
NatWest has advised customers on social media that it has "no timeframe" for a fix, but said its team is "working hard" to resolve it.
Customers are being advised to access their accounts in other ways if they can - such as through online banking.
However, some people have reported problems with NatWest's online service too, with one sharing an error message which they said was displayed when they tried to make a payment.
Others have expressed frustration with the bank's response, with one saying it was "disgraceful" there was no timeframe, while another called it "very poor service".
"What I don't get is the bank closes loads of branches 'to save money' and forcing people to rely on the app and online banking... but clearly hasn't invested in a system that works properly," one angry customer said.