"While we would like to keep the circumstances private, please know that he was surrounded by his family and was at peace," the statement added.
Norris, a six-time undefeated World Professional Middleweight Karate champion, had been hospitalised in Hawaii on Thursday, Variety magazine reported.
“To the world, he was a martial artist, actor, and a symbol of strength. To us, he was a devoted husband, a loving father and grandfather, an incredible brother, and the heart of our family,” the statement said. “He lived his life with faith, purpose, and an unwavering commitment to the people he loved.”
Norris rose to fame in the 1980s, starring in more than two dozen films, often portraying tough lawmen, soldiers and lone heroes.
His credits include Code of Silence, Missing in Action and The Delta Force, as well as the TV series Walker, Texas Ranger.
He also appeared alongside Bruce Lee in The Way of the Dragon and later starred with Sylvester Stallone, Arnold Schwarzenegger, Bruce Willis and Jean-Claude Van Damme in the 2012 film The Expendables 2.
His on-screen persona as an indestructible fighter later inspired a wave of internet memes about his toughness.
Norris’ films grossed millions of dollars and made him a popular figure among US troops. He visited Iraq in 2006 and 2007 to show support for American forces, the Reuters news agency reported.
A longtime supporter of conservative politics, he also authored several books with Christian and patriotic themes, according to Variety.
He is survived by his second wife, Gena O'Kelley, whom he married in 1998, as well as three sons, two daughters and a number of grandchildren.
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Source: Reuters, Variety, PAP