The statue of Felix Dzerzhinsky, the Bolshevik revolutionary nicknamed Iron Felix, stood outside KGB headquarters in Moscow until it was toppled by protesters in 1991 when the Soviet Union was heading to its breakup.
Images of demonstrators dismantling the towering figure with the help of a construction crane were among the most iconic symbols of the Soviet collapse.
Since then, Dzerzhinsky's statue has remained in a downtown park along with other sculptures of Soviet leaders removed from their locations.
The main KGB successor, the FSB, has its main headquarters in the imposing building on Moscow's Lubyanka Square.
The decision by the city legislature today allowed the Communist Party to go ahead and collect the nearly 150,000 signatures needed to hold a referendum in September.
However, Moscow Election Commission spokesman Dmitry Reut said later that it wouldn't allow the collection of signatures to start. Speaking to the Interfax news agency, he pointed at a law allowing the commission to act in such a way and said it would formally refuse tomorrow to register a group that would collect signatures for holding the vote.