Triple Olympic champion Bolt and new 100m world champion Blake were part of the Jamaican 4x100m relay team who had just won gold in a new world record time.
But they were widely criticised back home and accused of disrespecting Jamaica's national anthem after fooling around during the medal ceremony.
“As an ambassador for the sport and my country, I know my responsibilities and I will never do anything to put that in jeopardy,” said a statement on behalf of Bolt.
Blake also issued a statement through his manager.
“I realise that my actions during the playing of the national anthem could be interpreted as being disrespectful,” it said.
“This was certainly not my intention as I had only just competed at the very highest level and was still overjoyed.”
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