According to Pressley, the comedian filed a lawsuit on Monday in California, alleging that Johnson has made "false, malicious, opportunistic and defamatory accusations" that he drugged her nearly three decades ago.
Cosby is seeking compensatory and punitive damages, a retraction of her statements, and the removal of the chapter from her memoir in which the incident is mentioned. He also wants unsold copies of her memoir removed from circulation.
Johnson said in a statement that she was aware of the suit.
"I am aware of the statements from Bill Cosby," she said. "In cases of rape and abuse, abusers will do whatever they can to intimidate and weaken their victims to force them to stop fighting. I ask for your support of all of the victims involved. Thank you."
Last year, the model, 63, wrote that in 1986, Cosby invited her to his New York City brownstone to discuss a possible role in "The Cosby Show." There, she said, he gave her a cappuccino that had been spiked with drugs and put his hand around her waist. After that, she left, but said in an interview this year, "I knew that the kind of person I was dealing with would destroy me."
Since 2014, Cosby, 78, has been accused of drugging and/or sexual misconduct by more than 50 women. His attorneys have made numerous denials of wrongdoing and Cosby has never been charged with a crime.
Last week, Cosby filed a defamation counter-suit against seven women who had previously accused him of sexual misconduct and filed a defamation lawsuit against him. Cosby accused them of making "malicious, opportunistic and false and defamatory" comments and causing damage to his reputation and career. The women's lawyer called Cosby's lawsuit "a standard defense attorney’s play."
"My seven clients intend to vigorously proceed with their case and move forward as expeditiously as possible to get their day in court because each one of them are confident that their good name and reputation will be restored at the end of the day," Joseph Cammarata told ABC News at the time. "They will be found to be the truth-tellers."