The 86-year-old actor was best known as the star of the classic sitcom "The Andy Griffith Show" and legal drama "Matlock." His film credits include "A Face in the Crowd," "No Time For Sergeants," "Angel in My Pocket," "Adams of Eagle Lake," "The Treasure Chest Murder," "Hearts of the West," "Spy Hard," "Waitress" and "Playing the Game."
A representative for Twiford Funeral Homes in Manteo, N.C., told TMZ he was was buried at 11:30 a.m. EDT on his family farm on Roanoke Island in keeping with his wish to be buried immediately after death.
The celebrity news Web site said Griffith's burial followed a small, private service for close friends and family members.
No cause of death has been announced but Oscar-winning director Ron Howard, who played Griffith's son, Opie, as a child on "The Andy Griffith Show," told Deadline.com Griffith "has not been well for some time."
"His love of creating, the joy he took in it whether it was drama or comedy or his music, was inspiring to grow up around," Howard told Deadline. "The spirit he created on the set of 'The Andy Griffith Show' was joyful and professional all at once. It was an amazing environment."
U.S. President Barack Obama released a statement saying he and the first lady were saddened to hear about Griffith's death.
"A performer of extraordinary talent, Andy was beloved by generations of fans and revered by entertainers who followed in his footsteps," the president's statement said. "He brought us characters from Sheriff Andy Taylor to Ben Matlock, and in the process, warmed the hearts of Americans everywhere. Our thoughts and prayers are with Andy's family."
Tanya Jones, executive director of the Surry Arts Council, which oversees the Andy Griffith Museum, told The Charlotte Observer Griffith "means the world to the arts everywhere -- not just here in Mount Airy."
"We are blessed to have known him. We will cherish is his art, his music, his talent, and of course, our beloved 'Andy Griffith Show,'" Jones said.
Griffith was back in the spotlight this past May when he spoke warmly about his "Andy Griffith Show" co-star George Lindsey, who had recently died.
"Our last conversation was a few days ago," Griffith said in a statement at the time. "We would talk about our health, how much we missed our friends who passed before us and usually about something funny. I am happy to say that as we found ourselves in our 80s, we were not afraid to say, 'I love you.' That was the last thing George and I had to say to each other. 'I love you.'"
MSNBC said Griffith is survived by his wife Cindi and his daughter Dixie. His son Andrew Jr., known as Sam, died in 1996.
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