The social media giant has been repeatedly criticized by many, including President Trump, over claims that it systematically bans right-wing voices or content. Twitter denied allegations of "shadow banning" based on political viewpoint or ideology in a blog post last July.
The three accounts named in the lawsuit often interacted with and promoted each other on the platform in a seemingly organized way, says the suit.
Twitter hasn't commented on the lawsuit.
"This was an orchestrated effort", Nunes said during an interview with Fox's Sean Hannity on Monday.
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The school children were gathered outside the Al Noor mosque in Christchurch, where a white supremacist massacred 50 Muslims. Police have said the teenager - who can not yet be named - was not involved in the attack on two mosques.
"Twitter's use of its platform as a portal for defamation by political operatives and their clients runs contrary to every tenet of American Democracy, including the guarantees of both the First Amendment and Article I, § 12 of the Virginia Constitution", the suit claims. The congressman blames Twitter for allowing them to have a platform, and demands that the social media company remove defamatory messages.
He accused Mair and the two other accounts of engaging in a "concerted defamation campaign" to "cause huge pain" and divert his attention from leading the House Intelligence's probe into Russian meddling in the 2016 election.
"Twitter's actions also detracted from Nunes' investigation into corruption and Russian involvement in the 2016 Presidential Election", the lawsuit says.
The @DevinNunesMom account was "a person who, with Twitter's consent, hijacked Nunes' name, falsely impersonated Nunes' mother, and created and maintained an account on Twitter (@DevinNunesMom) for the sole objective of attacking, defaming, disparaging and demeaning Nunes", according to the complaint.
The lawsuit says those accounts were created for the sole goal of tweeting and retweeting false and defamatory statements about Nunes to "interfere with his duties, employment and investigations of corruptions as a United States Congressman".
Per the complaint, the account @DevinCow has no such disclaimer and caused Nunes "extreme pain and suffering" by calling him a "treasonous cowpoke" and an "udder-ly worthless" criminal.
Twitter CEO Jack Dorsey has acknowledged that the company's user bans have been too aggressive in some cases.
"Twitter's actions affected the election results". But fear not, we will win anyway, just like we did before!' Trump tweeted.