The prime minister, braving cold weather, stood for a few minutes before the flamewhichilluminates a bronze inscription that reads "Your name is unknown, your deed is immortal" at the memorial.
A Russian military band played, as Modi laid the wreath at the memorial.
The remains of the unknown soldiers killed in the Battle of Moscowin 1941 were initially buried in a mass graveof the Shtyki Memorialat the 40th km of the Leningrad highway at the city of Zelenograd.
The Tomb of the Unknown Soldier was designed by architects D I Burdin, V A Klimov, Yu R Rabayev and sculptor Nikolai Tomsky.
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The memorial was unveiled to the public on May 8, 1967.
The dark red porphyrymonument is decorated with a bronze sculpture of a laurelbranch and a soldier's helmet laid upon a banner.
The torch for the memorial's Eternal Flame was transported from Saint Petersburg where it had been lit from the Eternal Flame at the Field of Mars.
To the right of the tomb, there is a granite alley made of porphyry plates with encapsulated soils from hero cities, Saint Petersburg, Kiev, Volgograd, Odessa, Sevastopol, Minsk, Kerch, Novorossiysk, Tula and Brest.
The plate for Volgograd has since been changed to Stalingrad, the city's name during the Second World War.