The prime minister said the two consulates will facilitate travel and business cooperation with Russia.
Modi arrived in Moscow on Monday on a visit to attend the 22nd annual India-Russia Summit.
Before departure, the Indian leader said that he was looking forward to meeting President Vladimir Putin and described him as a friend.
Modi noted that the Special Privileged Strategic Partnership between the two countries has evolved over the last ten years, including energy, security, trade, investment, health, education, culture, tourism, and people-to-people exchanges.
He added that India and Russia seek to play a supportive role in a peaceful and stable region.
Putin and Modi met informally in Novo Ogariovo on Monday evening.
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