The activists released a video condemning the gun attack at the satirical magazine Charlie Hebdo which left 12 people dead.
In the clip, which was uploaded to the group’s Belgian YouTube account, a figure wearing the group’s Guy Fawkes mask and a hood says in French in an electronically-distorted voice: “We are declaring war against you, the terrorists.”
Sitting at a desk and reading from a piece of paper, the figure says the group will track down and close all accounts on social networks related to terrorists to avenge those killed.
The hashtag £OpChalieHebdo – presumably meaning Operation Charlie Hebdo – also appears on screen.
The group also reportedly published a statement on text-sharing website Pastebin, entitled “Message to the enemies of freedom of expression”.
In it they wrote: “Freedom of expression has suffered inhuman assault ... It is our duty to react ... We wish to express our condolences to the families of the victims of this cowardly and despicable act.”
They added: “We will fight always and everywhere the enemies of freedom of expression ... Freedom of expression and opinion is a non-negotiable thing. To tackle it is to attack democracy ... the struggle for the defence of those freedoms is the foundation of our movement.”
Anonymous has previously carried out cyber attacks on websites belonging to Governments, as well as those of corporate and religious organisations.