Michael Douglas "misses" his dad, Kirk Douglas

Michael captioned his post: "Happy Birthday Dad! I miss you and thank you for always giving the best advice! Love, Michael."

In the video, he said: "The best advice my father gave me was, 'Whatever you do, you do it to the best of your ability. You leave that job knowing that you couldn't have done any more, and then walk away, you've done the best. Don't look back.'"

Michael's wife, Catherine Zeta-Jones, also paid tribute to her beloved father-in-law.

She shared a black and white picture of Kirk kissing her cheek and wrote: "Missing you every day. Happy birthday Pappy [heart emojis] (sic)"

In May, the 76-year-old actor remembered the 'Spartacus' star as "one of a kind" and was pleased to have known his dad was proud of him.

Michael said: "There wasn't anyone like him. There's another generation, that was the great generation, post-World War II…and Dad was one of a kind.

"I think he's very happy. I know he takes particular pride -- not so much in whatever I worked with and I'm doing with the Motion Picture Television Fund -- but I know he loves Catherine [and] the work that she's doing.

"He always used to tease me. We would call him up and he would be like, 'Enough with you, let me talk to your wife.' He was a flirt until the very end."

Michael previously announced Kirk's passing in a statement on behalf of the whole family.

He said in a statement: "It is with tremendous sadness that my brothers and I announce that Kirk Douglas left us today at the age of 103. To the world, he was a legend, an actor from the golden age of movies who lived well into his golden years, a humanitarian whose commitment to justice and the causes he believed in set a standard for all of us to aspire to. But to me and my brothers Joel and Peter he was simply Dad, to Catherine, a wonderful father-in-law, to his grandchildren and great grandchild their loving grandfather, and to his wife Anne, a wonderful husband. Kirk's life was well lived, and he leaves a legacy in film that will endure for generations to come, and a history as a renowned philanthropist who worked to aid the public and bring peace to the planet. Let me end with the words I told him on his last birthday and which will always remain true. Dad- I love you so much and I am so proud to be your son."