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He made the remarks while attending the Italian premiere of latest Bond instalment Quantum of Solace.
Speaking at a press conference, he said: "After Barack Obama's victory I think we might have reached the moment for a coloured 007.
"I think the role is well suited to a coloured actor because the character created by Ian Fleming in the 1950s has gone through many changes.
"However, I think that this eventuality would probably make Fleming turn in his grave."
Craig went on to praise the US President-elect after his victory, saying: "It's as if we have sent a man to the Moon again. It's a very positive moment and wakes the whole world.
"I am a true fan of Obama and always have been because the political ideas that come out of his speeches have always seemed to be authentic."
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