Around two million people use the service and the problem has also affected customers of Royal Bank of Scotland (RBS) and Ulster Bank, which are part of the same group.
All the banks belong to RBS Group, which apologised to customers and said it was working to fix the problems which have prevented people from logging in.
The hitch is thought to have started at around 7am and is the latest technical problem to have beset the group, starting with a huge IT meltdown last summer.
A spokeswoman for RBS could not say how many customers have been affected, although both personal and business users have been hit by the problems, which have struck just before the busy Easter weekend as people make plans to get away.
There are more than two million active users of the app among RBS and NatWest personal banking customers alone, with 13 million log-ins taking place each week.
The latest IT issues come just three weeks after a hardware fault prevented RBS Group customers from using cash machines and also affected online and telephone banking services.
The group took a £175 million hit as a result of last summer’s IT chaos which left NatWest, Royal Bank of Scotland and Ulster Bank customers locked out of their accounts. The bulk of the redress costs related to Ulster Bank, where the problems took weeks longer to clear up.
A statement from RBS Group said: “We are aware of a technical problem this morning which is preventing customers from logging in to our mobile banking applications.
“We are working to fix the problem and apologise to customers for the inconvenience caused. No other systems are affected.”
The collapse also comes just weeks after the bank unveiled a new mobile banking feature for RBS/NatWest customers called Pay Your Contacts, which allows them to send payments of up to £100 to anyone with a Visa card, by entering their mobile number.
Last October, NatWest had to suspend another feature on its mobile phone app called GetCash, after the service was subject to a spate of “phishing” attacks by fraudsters.
The GetCash service, which allows customers to withdraw cash without using a debit card, was later re-instated after security was beefed up.
Customers vented their anger at being let down again by the group’s technology.
One Twitter user wrote: “No access to my iPhone app think it’s time to change banks!”
Another said: “The one day I’m desperate to use the NatWest app it’s broken, get it together people.”
Pointing out the bank’s previous IT problems, another Twitter user wrote: “How many chances do they want? After last time you would think they’ve learned.”
A spokeswoman for consumer group Which? said the problems will raise wider questions about “how robust and up to date banks’ IT systems are”.
She said: “Consumers and businesses alike rely on mobile banking services to access their accounts and consumers will rightly want to be assured that their money is accessible and safe at all times.”