Europe is furious about allegations that the U.S. government has been bugging European embassies and missions in apparent violation of a 1961 convention on diplomatic relations.
It remains unclear how the world's most famous refugee would be able to leave the transit zone of Sheremetyevo Airport, where he has been marooned without valid documents since he arrived from Hong Kong on June 23.
Venezuela's Maduro said he was offering asylum so that the former National Security Agency contractor could live "free of imperial North American persecution."
Vladimir Putin, who has disagreed with the Obama administration on its handling of the Syrian conflict and plans to develop a missile-defense shield in Europe, tried to distance himself from the case.