Indian PM Narendra Modi and Russian President Vladimir Putin are set to hold talks, with a firm focus on defence and nuclear energy co-operation
Mr Modi began his two-day visit on Wednesday with a private dinner with Mr Putin.
These talks have been held annually since 2000 and hosted alternately between Moscow and Delhi.
Russia and India were close allies during the Cold War, but recently the relationship has become more complex.
Bilateral trade between the two countries stands at $10bn (£6.74bn) and Russia is India's second largest defence supplier.
But earlier this year, India was reported to be displeased with Russia for selling attack helicopters to Pakistan and Russia was unhappy with India for choosing French Rafale fighters and American Apache attack helicopters over Moscow's defence products.
Mr Modi's visit is seen as a chance to work on the personal chemistry between the two leaders, and to reset relations between their countries, says the BBC's Sarah Rainsford in Moscow.
India has become an even more important market for Russia since the West imposed economic sanctions, our correspondent says, adding that Moscow is looking to sell India its sophisticated S400 anti-aircraft systems.
A deal to manufacture military helicopters and build further nuclear power plants in India could also be signed.
Last year, Russia announced it would help India build at least 10 more nuclear reactors. It has already built in a nuclear reactor in Tamil Nadu state.
The two countries have outlined an "ambitious vision" for nuclear energy and agreed that the new reactors would be built over the next 20 years.