Snowden is wanted by the United States on espionage and theft charges for allegedly leaking classified information about the National Security Agency's surveillance program.
Last week, Russia granted Snowden a temporary, one-year asylum, amid protests from the U.S. government.
RIA Novosti reported the head of the Federal Migration Service's regional branch in Moscow, Oleg Molodiyevsky, said Snowden is free to travel around Russia, but he must notify authorities before moving.
"In accordance with the law, he has the right to move around Russia's territory, and has the right to work, except, of course, in state offices," he said.
Migration authorities did not comment on where Snowden is now, RIA Novosti said.
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