A hacker calling himself "Bass" spoke to CBS News partner network Sky News via web video link -- the first time any of the group's members have appeared on camera -- albeit disguised with a facemask and sunglasses.
Bass told Sky that Anonymous had mobilized a team of 9,000 volunteers for the last attack, which temporarily brought down the sites of U.S. credit giants MasterCard and Visa, and also disabled the site of PayPal for a matter of hours.
All three companies stopped processing payments to WikiLeaks, reportedly under pressure from U.S. politicians.
"The software itself has been downloaded over 300,000 times," Bass told Sky, describing the tool his group has used to launch Distributed Denial of Service (DDOS) attacks on the corporations listed above, and others.
A DDOS attack uses thousands of computers to essentially bombard a website with requests for information all at once, eventually crashing the servers behind the website in question. Bass likened it to thousands of computers trying to open a given website and hitting "refresh" thousands of times per minute, all simultaneously.
The hacker vowed the attacks would continue, but said Anonymous chooses its targets carefully.
"Someone proposes the target, we've run intelligence on them, on what we consider the pros and cons of every target and a lot of other factors involved."
He said Anonymous had not and would not attack news media or social networking websites, even if those sites took action against or reportedly negatively on the hackers' actions.
Bass appeared via video link from an unknown location. Launching DDOS attacks is a cyber crime in both the United States and Britain.