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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In a wide-ranging Peston on Sunday interview, he said Parliament security needs reviewing and the PM's counter-terror strategy is flawed.
The star celebrated his 70th birthday with his family before attending a celebrity-filled bash held in his honour.
Douglas Carswell told ITV's Peston On Sunday he wanted to "support" the government as a "critical friend" but refused to rule out a return.