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Canadian-born Nielsen started out as a serious actor but in 1980, his role as a hapless doctor in the disaster spoof film Airplane! made him a comic star.
In all, he appeared in more than 100 films and had a star on Hollywood's Walk of Fame. "With his friends and his wife by his side, he just fell asleep and passed away," his nephew Doug Nielsen said, the AFP news agency reported.
'Don't call me Shirley', born in the Canadian city of Regina in 1926, Leslie Nielsen enjoyed an acting career which spanned six decades. He started as a television actor in New York in 1950, performing in about 150 live dramas.
In the mid-1950s, he moved to Hollywood, where he initially carved out a film career as a leading man, capitalising on his craggy good looks and 6ft2in (194cm) height.
Then in 1980 his deadpan delivery in the comedy disaster movie Airplane! marked him out as a gifted clown, says the BBC's Rajesh Mirchandani in Los Angeles.
It was in this role that he became known for the line "Don't call me Shirley".
The success of Airplane! led to another TV role in the spoof crime show Police Squad where he first played accident-prone detective Frank Drebin.
He went on to make three films as the same character in the Naked Gun series, starring opposite Priscilla Presley.
He continued working into his eighties.
Nearly two weeks ago - at the age of 84 - Nielsen was taken into hospital in Florida where he lived, suffering from pneumonia.
His condition had worsened over the last two days and relatives said he passed away peacefully, our correspondent says.