Speaking at the start of their meeting in the Kremlin, Modi lauded Russia for being "a reliable friend" who has "always stood by us."
Russia and India have shared close ties since Cold War times, when Moscow was a key ally and the main arms supplier to New Delhi.
Putin voiced strong support for New Delhi's aspirations to win a permanent seat at the U.N. Security Council, praising India's "well-balanced and responsible foreign policy course."
Trade between India and Russia, just below $10 billion in 2014, fell by more than 14 percent this year. Putin blamed the decline on a drop in global oil prices, Russia's main export commodity, and said the two countries should develop closer industrial cooperation.
Russia has built a nuclear reactor at India's Kudankulam nuclear power plant and is now completing a second unit there.
Putin said Russia is preparing to start building another two atomic reactors and intends to build 12 nuclear reactors in India over 20 years, according to an earlier agreement. A deal signed by Russian and Indian officials after Thursday's talks envisaged that components for the Russian-built reactors will be produced in India.
"The pace of our cooperation in nuclear energy is increasing," Modi said. "The agreement today will increase Indian manufacturing contents in these reactors."
Putin said the two countries would also cooperate on designing a next-generation fighter jet and a transport plane.
Following the talks, officials from both countries signed a slew of agreements on manufacturing helicopters, prospective joint exploration of Russian oil resources, simplifying visas for businessmen and other issues.
(AP)
Russian President Vladimir Putin, right, listens to Indian Prime Minister Narendra Modi in the Kremlin, in Moscow, Russia, Thursday, Dec, 24, 2015. Modi is on a two-day official visit to Russia.
Russian President Vladimir Putin, left, shakes hands with Indian Prime Minister Narendra Modi in the Kremlin, in Moscow, Russia, Thursday, Dec, 24, 2015. Modi is on a two-day official visit to Russia.
Russian President Vladimir Putin, right, meets with Indian Prime Minister Narendra Modi in Moscow's Kremlin, Russia, Thursday, Dec, 24, 2015. Modi is on a two-day official visit to Russia.
Indian Prime Minister Narendra Modi, center, watches honour guards marching during a wreath laying ceremony at the Tomb of Unknown Soldier outside the Kremlin Wall in Moscow, Russia, Thursday, Dec, 24, 2015. Modi is on a two-day official visit to Russia.
Indian Prime Minister Narendra Modi, left, watches honour guards marching during a wreath laying ceremony at the Tomb of Unknown Soldier outside the Kremlin Wall in Moscow, Russia, Thursday, Dec, 24, 2015. Modi is on a two-day official visit to Russia.
Indian Prime Minister Narendra Modi, center, takes part in a wreath laying ceremony at the Tomb of Unknown Soldier outside the Kremlin Wall in Moscow, Russia, Thursday, Dec, 24, 2015. Modi is on a two-day official visit to Russia.
Indian Prime Minister Narendra Modi listens to Russian President Vladimir Putin in the Kremlin, in Moscow, Russia, Thursday, Dec, 24, 2015. Modi is on a two-day official visit to Russia.
Indian Prime Minister Narendra Modi, left, watches honour guards marching during a wreath laying ceremony at the Tomb of Unknown Soldier outside the Kremlin Wall in Moscow, Russia, Thursday, Dec, 24, 2015. Modi is on a two-day official visit to Russia.
Indian Prime Minister Narendra Modi, right, takes part in a wreath laying ceremony at the Tomb of Unknown Soldier outside the Kremlin Wall in Moscow, Russia, Thursday, Dec, 24, 2015. Modi is on a two-day official visit to Russia.
Russian President Vladimir Putin, right, and Indian Prime Minister Narendra Modi attend a meeting with Russian and Indian officials and businessmen in the Kremlin in Moscow, Thursday, Dec. 24, 2015.
Russian President Vladimir Putin, right, and Indian Prime Minister Narendra Modi arrive to attend a meeting with Russian and Indian officials and businessmen in the Kremlin in Moscow, Thursday, Dec. 24, 2015.
Russian President Vladimir Putin, right, and Indian Prime Minister Narendra Modi arrive to attend a meeting with Russian and Indian officials and businessmen in the Kremlin in Moscow, Thursday, Dec. 24, 2015.
Indian Prime Minister Narendra Modi attends a meeting with Russian and Indian officials and businessmen during his meeting with Russian President Vladimir Putin in the Kremlin in Moscow, Thursday, Dec. 24, 2015.
Russian President Vladimir Putin attends a meeting with Russian and Indian officials and businessmen during his meeting with Indian Prime Minister Narendra Modi in the Kremlin in Moscow, Thursday, Dec. 24, 2015.
Russian President Vladimir Putin, foreground right, and Indian Prime Minister Narendra Modi, foreground left, arrive to attend a meeting with Russian and Indian officials and businessmen in the Kremlin in Moscow, Thursday, Dec. 24, 2015.