His publicist confirmed the news.
Demme, who also directed the Oscar winning film "Philadelphia" was suffering from esophageal cancer, publicist Annalee Paulo said in a statement.
She said he died in New York on Wednesday morning surrounded by his family.
Demme's most recent film was the 2015 comedy "Ricki and the Flash," starring Meryl Streep as an ageing rocker.
New York-born Demme won the directing Oscar for the 1991 thriller "The Silence of the Lambs", which also won Oscars for best picture and for its stars Anthony Hopkins and Jodie Foster.
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