"The vast majority of customers are not impacted and customer information remains safe," said Bridget Braxton, a spokeswoman for the fourth-largest U.S. bank by assets. Customers who have trouble should try logging in again because the disruption is usually intermittent, she said.
(Read More: Cybersecurity Firm Says It Is Under Attack )
Since September, a hacker activist group called the Izz ad-Din al-Qassam Cyber Fighters has said it was launching denial of service attacks against major U.S. banks. These attacks can disrupt service by deluging websites with high traffic.
In a posting Tuesday on pastebin.com, the group listed Wells Fargo as one of the banks "being chosen as a target." In December, Wells customers had trouble accessing the website for four days.
In its annual report filing last month, Wells said it had not experienced any "material losses" related to cyber attacks but that enhancing its protections remained a priority.