An online offensive against the so-called Islamic State (IS) led by the hacker-activist group Anonymous has taken down more than 5,000 Twitter accounts linked to the terrorist group as of Tuesday, Anonymous is claiming.

On Monday, the hacker-activist collective reported having taken down more than 3,500 pro-IS Twitter accounts.

Early Wednesday morning OpParis, which appears to be the official Twitter account of Anonymous' operation against online IS supporters, said that its communication channels were down after what it speculated might be counter-cyber attacks. The operation's Pastebin site, which collected web addresses of IS-affiliated websites, servers, and social media accounts, was also reported down "due to vulnerabilities," according to Anonymous.

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The OpParis account claimed that its servers and web communication channels were also under attack. Following the Anonymous group's announcement that it would target IS social media accounts, some observers warned that the attacks could trigger backlash not just from IS hackers, but also from hackers sympathetic to the extremist group.

"Retaliation on French-based companies following the Anonymous response to the attack in Paris is expected," read an alert from a security company called Radware, the Hill reports.

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The developments are the latest in a back-and-forth between the hacker group and IS militants, in the wake of the deadly string of attacks in Paris last week. On Tuesday, IS issued a response to Anonymous' threats, calling the hacker group "idiots."

"The #Anonymous hackers threatened in new video release that they will carry out a major hack operation on the Islamic state (idiots)," the statement reads. "What they gonna hack?"

OpParis acknowledged they were having some difficulty, according to their Twitter account, but did not miss an opportunity to lob an insult at whomever the hackers were attacking its servers.

Anonymous, which the Hill calls a "loosely affiliated collective," has launched other cyber attacks with mixed success. After the police shooting of Michael Brown in Ferguson, the group released the wrong name of the officer. Recently, the group released names of over 300 people who are allegedly in the Klu Klux Klan. ATTN: reached out to OpParis moderators for comment, but did not hear back before publishing this story.