Stephen Hester, the chief executive of NatWest owner RBS, has apologised for technical hitches which left customers unable to pay bills or access their money.
Announcing that the bank would open 1,200 branches nationwide tomorrow morning to clear a backlog of chaos caused by a problem with computer software, he said it had let down its customers.
Hundreds of customers have vented their frustration over the problems, with some finding payments had gone awry and others observing disappearing wages, or holidays and home purchases disrupted.
Account balances were not updated properly overnight, meaning credit and debit payments were not showing up as quickly as they should.
In a statement released tonight, Mr Hester said: "I am very sorry for the difficulties people are experiencing.
"Our customers rely on us day in and day out to get things right, and on this occasion we have let them down. This should not have happened.
"Right now my top priority, and the priority of the entire RBS Group, is to fix these problems and put things right for our customers.
"This is taking time, but I want to reassure people that we are working around the clock to resolve these problems as quickly as we are able."
Hester said that for the first time ever, NatWest would open 1,200 branches between 9am and noon tomorrow.
The bank said although the original technical glitch which caused the problems had been fixed it was working through the build up of transactions which had not been processed.
Concerns were raised over penalty charges, amid suggestions thousands of customers could be hit with fines if their regular household bill payments - including mortgages - are affected.
The issues extend to users of Royal Bank of Scotland (RBS) and Ulster Bank, which like NatWest are part of RBS Group.
Mr Hester added: "I also want to be clear that where our customers are facing hardship or difficulty we can and will help them.
"Our staff have already helped thousands of customers to access cash and we will continue to provide this service on a 24 hour basis while we work to resolve the problems.
"I also want to reassure customers that no one will be left permanently out of pocket as a result of this, and again, they should contact us directly about this.
"We have double the usual number of staff in our call centres, and for the first time ever we will open 1,200 branches across the country on a Sunday from 9am to 12pm.
"Once again I am very sorry for the inconvenience."
In an email sent to customers earlier on Saturday, Natwest apologised and attempted to explain the problems:
"We apologise to all of our customers who have been affected by our current technical issues," it read.
"These resulted in money credited to customers accounts overnight not appearing in their balances as it should. This problem is strictly of a technical nature, we have fixed the initial problem and our priority has been to work round the clock to sort the backlog as soon as possible. "
The repercussions have extended beyond the banks' own clients, with one couple who are not NatWest customers left unable to move into their new home.
RBS customer Stephen Cheesewright told the BBC he couldn't access money to buy food for his children, saying: "My bank balance shows as zero. I am unable to access any money or transfer any money from my RBS account to transfer funds to my ex-partner for food for my kids."
NatWest has more than 7.5 million personal banking customers, but the group said it could not tell how many have been affected as it was not possible to know when they were expecting payments into their accounts.