Its sites went down for about an hour yesterday and Thursday evening after a "deliberate" surge in internet traffic aimed at its NatWest website, according to the lender. It issued a statement yesterday saying that sites were again running and there was no risk to customers.
A spokeswoman said: "Due to a surge in internet traffic deliberately directed at the NatWest website, customers experienced difficulties accessing some of our customer websites today. This deliberate surge of traffic is commonly known as a distributed denial of service (DDoS) attack.
"We have taken the appropriate action to restore the affected websites. At no time was there any risk to customers."
This comes just days after an embarrassing IT failure for the group on the busiest online shopping day of the year.
RBS boss Ross McEwan admitted it had failed to invest properly in systems for decades as he apologised for the glitch on Monday, which left customers of RBS and its NatWest subsidiary unable to use credit and debit cards for three hours, while the banks' websites and smartphone apps were also affected.
It came on so-called Cyber Monday, when retailers expected the highest number of online transactions to take place before Christmas - and prompted a flurry of card users to take to Twitter to vent their anger. The bank faces a multimillion-pound compensation bill after it accepted it should reimburse customers who faced extra costs or were unable to take advantage of discounts as a result of that IT failure.
An RBS source said at the time a key period of under-investment came during Fred Goodwin's time as chief executive between 2001 and 2009 when "money was spent on acquisitions rather than integrating and improving the systems".
RBS said yesterday's cyber attack was not related to the issues on Monday, adding that banks around the world are regularly subjected to this type of deliberate attempt to bring systems down and disrupt customer access. But the group has had a run of IT problems over the past two years.
In May, another glitch left RBS and NatWest customers using mobile apps unable to gain access to their accounts online.
That followed a major fiasco in June last year which saw payments go awry, wages appear to go missing and home purchases and holidays interrupted. It cost the group £175 million in compensation.
RBS said group sites were affected on Thursday night by the attack for around an hour, although its NatWest systems were more badly affected and were intermittent for four hours.
RBS was also fined this week for its part in forming illegal cartels to benchmark interest rates. The taxpayer-backed lender was among eight global banking giants, including Barclays and Deutsche Bank, fined a record €1.7 billion (£1.4bn) after a European Commission investigation into Libor-rigging.
On Thursday, the Archbishop of Canterbury criticised the "rotten culture" which afflicted Britain's banking industry, saying the "struggle" to change that mindset had begun but could take a generation to complete.
In a debate on reports by the Parliamentary Commission on Banking Standards, he told peers: "On the outcome of this struggle hangs, to a considerable extent, the flourishing of our society and the re-establishment of the reputation of our most successful industry."