Coppola says the story is false and libellous.
The suit, which seeks at least $15 million from the publication, was filed in Los Angeles Superior Court on Wednesday, two weeks before the director's long-dreamed-of and self-financed epic is to be released in US theatres.
The suit calls the director of The Godfather and Apocalypse Now a "creative genius" and says others are "jealous" and therefore tell "knowing and reckless falsehoods."
It says Variety's "writers and editors, hiding behind supposedly anonymous sources, accused Coppola of manifest incompetence as a motion picture director, of unprofessional behaviour on the set of his most recent production, Megalopolis, of setting up some type of scheme so that anyone on the set who had a complaint of harassment or otherwise had nowhere to lodge a complaint, and of hugging topless actresses on the set. Each of these accusations was false."
A spokesperson said Variety was standing by its reporters.
The July 26 story used anonymous reports and videos from Megalopolis crew members of the shooting of a nightclub scene in an Atlanta concert hall in February, 2023.
The story said Coppola tried to kiss young female extras and "appeared to act with impunity" on the set. It said the film's financial arrangements meant "there were none of the traditional checks and balances in place."
In one video, Coppola, wearing a white suit, walks through a dancing crowd, stopping to apparently lean in to several young women to hug them, kiss them on the cheek or whisper to them. Another video shows him leaning into a woman who pulls away and shakes her head.
In a subsequent story about a week later, one of the women, Lauren Pagone, told Variety Coppola left her "in shock" when he touched, hugged and kissed her without her consent.
Pagone said she came forward because another of the extras, Rayna Menz, said in Variety's sister publication Deadline that Coppola did nothing to make her or anyone else on the set uncomfortable.
The lawsuit takes particular issue with an assertion in the Variety story that Coppola inadvertently got into a shot and ruined it. The suit says Coppola was well aware that some camera angles would include him, and that he was supposed to appear in the scene anyway.
"The average reader would understand that Coppola was so aged and infirm that he no longer knew how to direct a motion picture," the suit says.
Megalopolis is a Roman epic set in a futuristic New York starring Adam Driver and Nathalie Emmanuel. Coppola sold off pieces of his considerable wine empire to largely finance it himself.
