As a result, the banks plan on opening branches for an extended period on Saturday and also on Sunday.
NatWest said: "Over 1,000 of our branches will be open until 7pm tonight to help customers with enquiries or who need access to their cash.
"In addition, our branches open on Saturday will extend working hours to 6pm, and these branches will also be open this Sunday from 9am to 12pm."
Susan Allen, Director of Operations at RBS Group told Sky News that the problem was sparked by a software failure.
"We know that a system outage on Tuesday caused this backlog," the bank said in a statement.
"While that outage has been resolved, the backlog itself is now the problem and RBS is working around the clock to resolve this."
The glitch is believed to have affected online balance facilities and credit updates into the accounts of up to 12 million customers at NatWest.
On Friday morning RBS Group tweeted: "Unfortunately we are once again experiencing technical issues with our systems and account balances have not updated properly overnight.
"This means where money has gone into a customers' account, there may be a delay in it appearing on their balance."
"We also recognise this is an unacceptable inconvenience for which we apologise."
NatWest said that no customers "would be left out of pocket because of the technical problems we have experienced" and encouraged account holders to contact customer services.
"I got the bus in to find none of them open and it was absolutely teeming down.
"I contacted customer services again and after 15 minutes of waiting on hold, I was told they didn't know which branches would be open.
"The staff in the branch were very helpful but I am now worried about what will happen to my mortgage payment next week."
On Thursday afternoon, RBS expected the fault to be fixed within two hours but later hinted that the problem could continue for an extended period.
Announcing the decision to extend branch hours, it tweeted: "This is to give our customers who need access to cash in advance of the weekend."