The incident took place in a bar in the Marais district of Paris where the Christian Dior designer had apparently been drinking. Galliano was detained by police on Thursday night on suspicion of assault and making anti-Semitic remarks and was released pending charges.
Speaking to AFP Galliano's lawyer Stephane Zerbib said the designer "formally denies the accusations of anti-Semitism made against him", going on to state that "legal action will be taken against those making such accusations".
Galliano is currently preparing for Paris Fashion Week where he will be showcasing collections for his own label as well as for Christian Dior.
Christian Dior representatives have yet to comment on the situation.
UPDATE: Christian Dior have suspended creative director John Galliano following the incident, pending an investigation.
Chief executive Sidney Toledano said in an official statement: "Dior affirms with the utmost conviction its policy of zero tolerance towards any antisemitic or racist words or behaviour. Pending the results of the inquiry Christian Dior has suspended John Galliano from his responsibilities."
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