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About 15-20 agreements are expected to be signed.
This is Mr Putin's first summit with Prime Minister Modi at a time when Russia is at odds with the West over Ukraine, and its economy is stalling as oil prices tumble to their lowest point in five years. The two leaders had met on the sidelines of the BRICS summit in Brazil in July and during the G-20 summit in Australia last month.
They are holding a one-on-one meeting followed by intergovernmental talks and will also preside over the signing of a broad "vision" document laying out a roadmap for cooperation over an extended period, officials on both sides said.
The close ties that India and Russia once shared are seen to have waned. Bilateral trade, at $10 billion, is now one-ninth of that between Russia and China. Moscow also recently sealed a military cooperation pact with Pakistan after lifting its embargo on arms supplies to that country and is in talks to supply Islamabad with combat helicopters.
The Russian president is seeking new markets for his country's natural resources as its economy reels under US and EU sanctions over its backing of an uprising in Ukraine and annexation of Crimea.
Since coming to power Modi has sought closer ties with US President Barack Obama, who has accepted an invitation to join India's Republic Day celebrations in January. But India has opposed joining the Western sanctions against Russia.
As President Putin arrived in Delhi yesterday, PM Modi tweeted in Russian, "Delighted to welcome President Putin to India. Looking forward to a productive visit that will take India, Russia ties to newer heights." He also said, "Times have changed, our friendship has not. Now we want to take this relation to the next level and this visit is a step in that direction."
Ahead of his visit, when asked about the perception that Russia-India ties have lost some warmth, Mr Putin described India as a "reliable and time-tested partner" and termed ties with New Delhi as a "privileged strategic partnership."
The deals today are expected to cover oil exploration and supply, infrastructure and an increase in direct diamond sales to India. Mr Putin is also pushing to supply more nuclear reactors. A 1,000-megawatt reactor is operating at the Russian-built Kudankulam power station in Tamil Nadu, with a second due to come onstream in 2015.
On defence, the two sides will seek to move ahead with long-delayed projects to develop a joint fifth-generation fighter jet and a multi-role transport aircraft. Russia is the largest supplier of weapons to India, the world's top arms buyer.
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