"Indiana Jones and the Kingdom of the Crystal Skull" stars Harrison Ford as an archaeologist competing in 1957 with an evil KGB agent, played by Cate Blanchett, to find a skull endowed with mystic powers.
It hit Russian screens Thursday.
Communist Party members in St. Petersburg said on a web site this week that the Soviet Union in 1957 "did not send terrorists to the States," but launched a satellite, "which evoked the admiration of the whole world."
Moscow Communist lawmaker Andrei Andreyev said Saturday "it is very disturbing if talented directors want to provoke a new Cold War."
