The family of George Harrison have asked his fans around the world to join them in a minute of meditation today as a tribute to the late Beatle.

His wife Olivia and son Dhani also expressed their thanks for the displays of affection following his death from cancer.

"We are deeply touched by the outpouring of love and compassion from people around the world," they said in a statement.

Harrison, 58, was cremated in a cardboard coffin only hours after his death in Los Angeles. His ashes will be scattered on a sacred Indian river.

The minute of meditation is scheduled for 9.30pm British time.