Linda Gray, a long-time friend who starred alongside him in the TV show, called him her "best friend for 35 years", her agent told the BBC.
"Larry was back in his beloved Dallas re-enacting the iconic role he loved most," his family said in a statement carried by the Dallas Morning News.
"Larry's family and close friends had joined him in Dallas for the Thanksgiving holiday. When he passed, he was surrounded by loved ones. It was a peaceful passing, just as he had wished for. The family requests privacy at this time."
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The actor was asked about black or mixed race role models and whether Markle's upcoming marriage to Harry would help inspire young people.