The First Amendment applies to the government, not to private companies like social media sites.
The lawsuit is in partnership with the America First Policy Institute.
Trump is seeking class action status for the suits.
“We’re not looking to settle,” Trump said.
Facebook and Google didn’t immediately respond to a request for comment.
Twitter declined to comment.
Twitterpermanently bannedTrump in January.
Facebook, Twitter and Google have all said that’s not the case.
The app was briefly hacked over the weekend.
CNET’s Joan Solsman contributed to this report.