"I'd like to offer my condolences to Her Majesty the Queen and the Royal Family," Smith, who played Prince Philip on the first two seasons of the Netflix show said in a statement to Us Weekly.
"Prince Philip was the man. And he knew it. 99 and out, but what an innings. And what style. Thank you for your service old chap - it won't be the same without you," Smith added.
Philip died the morning of April 9 at Windsor Castle. He was 99.
Menzies, who took over the role of Prince Philip on the following two seasons of "The Crown," shared a quote from Shakespeare on social media.
"If I know anything about the Duke of Edinburgh I'm fairly sure he wouldn't want an actor who portrayed him on TV giving their opinion on his life, so I'll leave it to Shakespeare. 'O good old man! how well in thee appears The constant service of the antique world...' RIP," Menzies tweeted.
Smith and Menzies are two of many celebrities and public figures, ranging from Sir Richard Branson to "Star Trek" actor George Takei, who have shared their reactions to the Duke of Edinburgh's death.
"Netflix, Left Bank Pictures, Sony Pictures Television and the production team on 'The Crown' are deeply saddened to hear of the death of The Duke of Edinburgh," the streaming service and production companies said in a separate statement. "Our thoughts are with the royal family at this sad time."
"The Crown" is set to start filming its fifth season this summer, which should cover the events of the early '90s.
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