Before the video was released, Mr Galliano had already been questioned by the police, last Thursday, after an incident at the bar, La Perle, in the trendy Marais district of Paris. He has been accused by two other clients — Geraldine Bloch, 35, and Philippe Virgitti, 41 — of making an anti-Semitic slur.

French law makes it a crime to incite racial hatred; the statute has been used in the past to punish anti-Semitic remarks. The French advocacy group SOS Racisme said that it would support legal proceedings if the accusations were confirmed. ‘‘Mr. Galliano has added to the ignominy of his words with the cowardice of a denial,’’ it said in a statement.

Mr. Galliano’s lawyer, Stéphane Zerbib, did not respond to requests for comment Tuesday. He has denied that Mr. Galliano made any anti-Semitic comments in the incident last week and has submitted testimonials of support from employees and witnesses at the bar as part of defamation complaints filed against Ms. Bloch and Mr. Virgitti. Mr Galliano and his partner, Alexis Roche, could not be reached for comment.

A police spokeswoman also declined to comment Tuesday, except to say that witnesses, including Mr. Galliano, had been questioned Monday in a police station in the third arrondissement of Paris, where the bar is located, and subsequently released. She referred all questions to the Paris prosecutor, who did not return calls seeking comment. According to French media reports, the police questioned the owner of La Perle, the bar’s security staff and other clients.

One person who witnessed last week’s incident at the bar — Lyes Meftahi, 38, a Parisian, who runs an audiovisual company — said that Mr Galliano was certainly drunk, speaking slowly and slurring his words. But he said that the designer was keeping to himself and was ‘‘provoked’’ by a woman, who had called Mr. Galliano ‘‘ugly.’’ Mr. Meftahi heard no anti-Semitic slurs and said that Mr. Galliano himself was threatened with violence at one stage during the altercation.