A banking group said it is "working round the clock" to fix technical problems for NatWest customers before the weekend begins.
Large numbers of customers have been affected by the hitches since Wednesday, and Royal Bank of Scotland (RBS) Group said that many will still only see yesterday's balances showing up on their accounts today.
Angry customers have vented their frustration about the problems, which are also affecting Royal Bank of Scotland and Ulster Bank users, with some finding that they had supermarket deliveries stopped and others having holidays or home purchases disrupted.
Account balances are not being updated properly overnight, meaning that credit and debit payments are not showing up as quickly as they should, although an RBS Group spokeswoman said the money is "in the system".
She said that even if people go into their branch, they may not see the most up-to-date information on their balances, although staff are "geared up" to help customers who are having problems using their accounts.
Fears have been raised that thousands of customers could be hit with penalty charges if their regular household bill payments such as mortgage payments are affected.
The banking group has promised that no one will be out of pocket and the spokeswoman said that anyone who incurs such a penalty as a result of the problems should contact their branch.
Asked if the problems would be resolved by the weekend, the RBS Group spokeswoman said: "Our technicians are working round the clock. It is obviously a priority. That's what we're hoping to achieve."
NatWest has more than 7.5 million personal banking customers, but the spokeswoman said it was difficult to say how many have been affected as it was not possible to know when they were expecting payments into their accounts.
However, Ulster Bank said that around 100,000 of its customers have been affected by the same issues.
The problem reportedly arose after staff tried to install a software update on RBS's payment processing system, but ended up corrupting it.
RBS Group could not confirm this, but said they were "making progress" with the original technical issue.
With the bank's advertising slogan Helpful Banking attracting the attention of many tweeters, there were numerous messages on Twitter about wages not appearing in accounts or the prospect of being hit with late payment charges.
One user wrote: "£natwest what are u doing! I'm off on holiday today meant to get paid today so where's my money? helpful banking ay!"
Another said: "Due to complete on flat purchase today. All the money missing in cyberspace. Stressful enough without this, thanks £natwest."
First-time buyer Raul Poddy, 30, told BBC News that he, his pregnant wife and their one-year-old chid came close to spending a night in an empty home because of the problems.
He said that his family were due to complete the purchase of their first home but, because solicitors could not check that funds had been transferred, the keys were not immediately released.
They faced "throwing down a mattress" to spend the night in their empty, rented home in Durham until the problem was resolved, but the keys were later released, allowing them to move in.
Mother-of-two Lisa Browne said she had tried to get Tesco to deliver a weekly food shop to her home but the store said her NatWest bank card had been declined.
She said she was relying on her salary going into her account to keep her in credit and told the Daily Mail: "I'm really annoyed."
More than 1,000 NatWest branches in major towns and cities were kept open until 7pm last night and opened early at 8am today.
A statement placed by NatWest on its website today told customers: "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 customer's account, there may be a delay in it appearing on their balance.
"We can assure our customers that this problem is strictly of a technical nature and we continue to work hard to resolve this.
"We also recognise this is an unacceptable inconvenience for our customers, for which we apologise."
A spokeswoman for UK Payments Administration, which oversees payments generally, said the problem was not a central one and therefore it did not appear to have affected other banks.
But anyone expecting payments from people or businesses which bank with NatWest and RBS could encounter delays due to the technical issues at their end, she said.