The imam of the Great Mosque of Paris slammed the 34-year-old's salute after scoring a goal in Britain, saying he "strongly condemned any act or words of an anti-Semitic or racist nature in the sporting world."
The mosque's imam, Dalil Boubakeur, said the action -- known as "quenelle" in France -- was a "hybrid gesture between a Nazi salute and an inverted 'up yours' sign."
He said sports "represented the highly humanist and universal values of peace, friendliness and fraternity."
France's sports minister, Valerie Fourneyron, called it a "shocking, sickening provocation" and said there was "no place for anti-Semitism and inciting hatred on the football pitch".
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British media reported that the Football Association was investigating the incident and could risk sanctions, while the European Jewish Congress demanded English Premier League officials ban Anelka.
Anelka had thrust his straightened right arm downwards while tapping his bicep with the other hand after scoring a goal in a game between his West Bromwich Albion team and West Ham United.
The French comedian in question is Dieudonne M'Bala M'Bala, who has outraged French authorities and Jewish organisations many times with his frequent anti-Semitic tirades. He has been fined seven times for defamation, insult and provocation to hate, and for racial discrimination.
The comic, widely known by his first name, has popularised the straight-arm gesture, which he calls a "quenelle" -- a dumpling made of fish or meat. He says it stands for his anti-establishment views.