The shooter's motivations were not yet known.
Russia's Investigative Committee, which has opened a murder investigation, said a 50-year-old man from the village of Kratovo, on Moscow's southeastern edge, had shot at other residents from his house.
One person died in hospital and three bodies were found at the scene, the committee said in a statement, adding that a member of the National Guard had been injured.
Gunfire could be heard in footage aired on public television that showed the woodland area surrounded by police.
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