A total of 1,200 NatWest branches are opening on a Sunday for the first time ever, as the bank attempts to clear a huge backlog of payments caused by a computer glitch.
Stephen Hester, chief executive of NatWest owner RBS, has issued a public apology for the technical hitch and admitted the bank had let down its customers.
Branches were due to open their doors between 9am and noon, amid continued anger following days of disruption.
The chaos, caused by a problem with computer software, left many of its clients unable to pay bills or access their money.
Mr Hester strived to reassure customers following fears thousands of people could be hit with penalty charges if their regular payments - including mortgages - were affected.
"I am very sorry for the difficulties people are experiencing," he said.
"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."
NatWest has more than 7.5 million personal banking customers but it is unclear how many have been affected.
The issues extend to users of Royal Bank of Scotland (RBS) and Ulster Bank, which like NatWest are part of RBS Group.
Ulster Bank said about 100,000 of its customers experienced difficulties. While the original technical glitch has been fixed, staff are now working through the build-up of transactions which have not been processed.
