The suit, filed in federal court in Manhattan, seeks $75,000 in damages.
American pornographic actress Stormy Daniels last month came out with a sketch of a man, who had allegedly threatened her seven years ago over her affair with US President Donald Trump, media reports said.
The lawsuit adds a new complication to litigation involving Trump and his personal lawyer Michael Cohen, who paid Daniels $130,000 just before the 2016 United States presidential election to keep quiet about her alleged relationship with Trump.
According to the complaint, which was released on Twitter Monday by Avenatti, Trump's Twitter remark is "false and defamatory" and "falsely attacks the veracity of Ms. Clifford's account of the threatening incident that took place in 2011". Daniels claims the man approached her and her infant daughter in a Las Vegas parking lot and tried to intimidate her into staying silent. He has said the $130,000 payment was legal.
The whole saga broke out in March when Daniels, at a television interview, said she was threatened to be quiet over the affair in 2011.
The litigation focuses on a tweet from Trump on April 18. She told CBS News' 60 minutes programme that following the end of the relationship, a man approached her and her daughter in a Las Vegas vehicle park and told her to "forget the story, leave Donald Trump alone". "And then he leaned around and looked at my daughter and said, 'That's a handsome little girl".More news: Vettel heads Hamilton in Baku FP3
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It adds that he "knew that his false, disparaging statement would be read by people around the world, as well as widely reported".
Cohen did not work for Trump's 2016 campaign and it is illegal for a campaign under FEC rules to spend funds on personal matters, so these allegations are serious.
A Los Angeles judge on Friday put Daniels' lawsuit there against Cohen and Trump to end her non-disclosure agreement on hold for 90 days.
Cohen asked for a delay after Federal Bureau of Investigation agents raided his home and office several weeks ago. She contends the agreement is invalid because Trump never personally signed it.
Ms Daniels has also accused Mr Cohen of defamation over a separate statement he made in February.