According to a report in Fox News late Monday, Nunes said he was going after Twitter first because they "are the main proliferator" of "fake" and "slanderous" news.
"The case we're basically making is this was an orchestrated effort. So people were targeting me, there were anonymous accounts that were developed... and these accounts are not supposed to exist. Twitter says that they don't have accounts that do this," Nunes was quoted as saying.
"They need to come clean. They're not a public square. They are content developers," he added.
The lawsuit accused Twitter of "shadow-banning conservatives" to influence the 2018 mid-term election.
Twitter CEO Jack Dorsey, in his testimony before Congress last year, said his platform is a kind of "digital public square".
Nunes questioned why the company would allow certain accounts to attack him "hundreds of times a day".
Twitter was yet to comment on the lawsuit.
US President Donald Trump last year slammed Twitter for "shadow banning" some Republicans in search results on the micro-blogging platform.
The micro-blogging platform had said it is not involved in banning people based on political viewpoints and there was a technical issue in its search that has been resolved.