Cohen is a key witness in the criminal case against Trump for paying Stormy Daniels a 'hush share' during the 2016 election campaign.
Trump's supporters have been criticizing Cohen lately.
Cohen's spokesman and lawyer, Lanny Davis, told the BBC he believed the case would be settled in his client's favour.
"Trump appears to be abusing the judicial system once again by harassing and intimidating Michael Cohen. Trump fears punishment and may be trying to send a message to other potential witnesses collaborating with prosecutors against him," Davis said.
Cohen is also charged with "making inappropriate, manipulative and malicious statements about his former client, family and business" in the lawsuit filed in Florida Federal Court.
Cohen served as Trump's attorney for more than 10 years. He was also vice president of Trump's holding company, the Trump Organization, and has been described as "the man who has Trump's back".
But after the presidential election in 2016, there was a big disagreement with Trump when inspections of Trump's aides began.
Cohen pleaded guilty to fraud and campaign finance violations in 2018, was sentenced to 3 years in prison and a fine.
Cohen also came to the fore with his criticisms of Trump in the news programs he appeared after he was released from prison.
Some of the words of Cohen, who wrote a book and made a podcast, were also included in the petition filed by Trump.
Cohen is accused of unfairly calling Trump a "racist" in his 2020 book Infidelity.
Trump appeared before a judge in New York on April 4, on the grounds that he had falsely recorded his "hush share" payment to Daniels, and denied the charges.
Cohen admitted that he facilitated the payment of $130,000 to Daniels.