"He's a busy man, I'm a busy man, why should I invite him?" web portal Russia Today quoted Rogozin as saying on Saturday.
While Rogozin has not met Musk as yet, he frequently reacts publicly to the SpaceX CEO's tweets and slams SpaceX over "killing competitors."
Earlier in March, Rogozin congratulated Musk on the very first flight of the new reusable SpaceX ship - the Crew Dragon - to which Musk replied - "we have always admired your rocket and spacecraft technology".
Later, however, it emerged that Roscosmos complained to NASA, alleging the Crew Dragon brought a mysterious alcohol odour aboard the International Space Station (ISS), the report said.
The claim was made after the spacecraft itself was destroyed in a powerful blast during ground tests.