Modi began his visit Wednesday with a private dinner with Putin. More talks involving top officials from both countries are to be held in the Kremlin on Thursday.
Trade between India and Russia was just below $10 billion in 2014. The two countries have set an ambitious goal of increasing trade to $30 billion by 2025.
Russia and India have shared close ties since the Cold War, when Moscow was a key ally and the main arms supplier to New Delhi.
Indian Foreign Secretary S. Jaishankar told reporters ahead of the visit that Russia is a "very major military and strategic partner," adding that there will be discussions on more arms purchases for the Indian military, including a deal to manufacture 200 Kamov-226T helicopters in a joint venture located in India.
While India has remained a major customer for the Russian arms industry, the country in recent years has sought to diversify its purchases, buying military hardware from the United States, France and Israel.
Jaishankar said Modi's talks in Moscow will also include nuclear cooperation.
"We have a road map for nuclear cooperation with Russia, and we are moving in accordance with that," said Jaishankar.
Russia has built a nuclear reactor at the Kudankulam nuclear power plant in India and is now completing a second unit there. The two nations have a plan envisaging that Russia will build a total of 12 nuclear reactors in India over 20 years.
(AP)
Indian Prime Minister Narendra Modi, reviews an honour guard upon arrival at Moscow's Government Vnukovo II Airport outside Moscow, Russia, Wednesday, Dec. 23, 2015. Modi is on official visit and plans to meet Russian President Vladimir Putini on Thursday, Dec. 24, 2015.
Indian Prime Minister Narendra Modi, reviews an honour guard upon arrival at Moscow's Government Vnukovo II Airport outside Moscow, Russia, Wednesday, Dec. 23, 2015. Modi is on official visit and plans to meet Russian President Vladimir Putini on Thursday, Dec. 24, 2015.
Indian Prime Minister Narendra Modi, reviews an honour guard upon arrival at Moscow's Government Vnukovo II Airport outside Moscow, Russia, Wednesday, Dec. 23, 2015. Modi is on official visit and plans to meet Russian President Vladimir Putini on Thursday, Dec. 24, 2015.
Indian Prime Minister Narendra Modi, prepares to step off a plane upon arrival at Moscow's Government Vnukovo II Airport outside Moscow, Russia, Wednesday, Dec. 23, 2015. Modi is on official visit and plans to meet Russian President Vladimir Putini on Thursday, Dec. 24, 2015.
Russian President Vladimir Putin, right, greets Indian Prime Minister Narendra Modi during their meeting in the Kremlin in Moscow, Belarus, Wednesday, Dec. 23, 2015.
Russian President Vladimir Putin, right, and Indian Prime Minister Narendra Modi walk together during their meeting in the Kremlin in Moscow, Belarus, Wednesday, Dec. 23, 2015.
Russian President Vladimir Putin, right, and Indian Prime Minister Narendra Modi, left, walk together during their meeting in the Kremlin in Moscow, Belarus, Wednesday, Dec. 23, 2015.
Russian President Vladimir Putin, right, shakes hands with Indian Prime Minister Narendra Modi during their meeting in the Kremlin in Moscow, Belarus, Wednesday, Dec. 23, 2015.