"It has to be returned to where it belongs, among the collection of France's national heritage," said Jean-Noel Jeanneney, president of the Bibilotheque Nationale de France (BNF) on Tuesday.
The manuscript, known as Hebrew 52, is a complete Bible in Hebrew and believed to be one of the oldest surviving examples of the Pentateuch, or the five books of the Torah.
It had belonged to the French national collection since 1668.
It was allegedly stolen in 1998 by a trusted curator at the BNF, who apparently smuggled it out of the country to Britain using a customs authorisation form he had signed himself.
He is believed to have sold it for about $80,000.
The book eventually ended up in the US. It was sold by a third party through Christie's auction house in New York in May 2000 to a New Yorker called Josef Goldman for about $350,000.
The theft was discovered a few months later in July 2000, when a reader in Paris asked to consult the text and it could not be found.
After a long police inquiry, involving Interpol and with the help of Malachi Beit Arie, a former director of Israel's national library, the book was traced to New York.
In March 2006, curator Michel Garel, 57, who worked at the BNF for 28 years, was given a two-year suspended sentence for theft by a Paris court and ordered to pay damages to the French state.
He has appealed the sentence, claiming he has been made a scapegoat.
The BNF is pressing Goldman for the return of the book, with the help of New York-based attorney Pierre Cournot, who filed a suit with the Supreme Court in New York on May 26.
Goldman and Christie's were reported by the New York Post last month to have said they had not known the book was stolen when it was auctioned.