The hacker collective Anonymous claims it has already taken down 5,500 Twitter accounts in its cyber war against the militant group Islamic State (IS).

Anonymous released a video on Sunday saying they would “launch the most important operation ever carried out” against IS in retaliation for Friday's terrorist attacks in Paris, which killed at least 129 people and injured hundreds.

Announcing from its #OpParis account, Anonymous said Tuesday:

Over the past dozen years, Anonymous has been known for cyber attacks on government, corporate, and religious websites. But with increasing terrorism activities by fundamentalists such as Islamic State, Anonymous has been using its skills to wage a virtual war against IS and its online supporters.

As Jaikumar Vijayan reported for The Christian Science Monitor:

Following the deadly attacks on the satirical newspaper Charlie Hebdo earlier this year, Anonymous launched a campaign dubbed #OpISIS to expose and destroy websites, social media accounts, and e-mail addresses of those it considered as affiliated with the terror group. Since then, it has claimed credit for shutting down several websites, and exposing e-mails, private networks, Internet addresses, and more than 9,000 Twitter accounts allegedly being used by Islamic State (ISIS) activists.

Once known as a puckish digital vigilante group, Anonymous now seems to be assuming some degree of civic responsibility. Earlier this month, the collective released a list of hundreds of names and social media accounts of Ku Klux Klan associates. Paul Williams, a hacktivist writer and occasional documentarian, writes of the group, “Anonymous had come to the conclusion that they were no longer abstractly playing with scatology and paedo bears.”

With its biggest operation against Islamic State already underway, shutting down IS social media presence, Anonymous says it's important to successfully weaken the group.

“They want to strike terror with their name, with bloody images, with violent videos. We cannot fight them with guns and rifles, stopping their propaganda is an effective way to weaken their manpower and their presence in the Internet. Disrupting their communications makes it difficult to organize their attacks in a fluid manner,” the person behind the Operation Paris account told the BBC.

In June, senior intelligence officials told Congress that Islamic State and other terrorist groups were increasingly using social media to attract new recruits in the United States.

“Unlike the centralized and secretive operations of Al Qaeda, Islamic State is successfully recruiting new members through aggressive use of social media, particularly Twitter,” the officials said.

The Christian Science Monitor reported that “estimates are that the terror group can generate up to 200,000 tweets per day based on the initial work of a couple thousand “core propagandists.”

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Will the new intensified campaign by Anonymous really have any impact at all on IS?

"Cyberattacks can have a tremendous impact," cyberwarfare expert David Gewirtz told CBS News. "Of course, they can't be used to arrest people or take terrorists off the field, but they can certainly be used to compromise structural components of terrorist operations. More to the point, they can go after both the money that terrorists have and their funding sources. Damaging the money flow can certainly have an impact on the terrorists' operations."