Here are the latest developments
After the meeting with President Putin, PM Modi tweeted, "Met President Putin and discussed India-Russia ties. The meeting was fruitful."
Despite the inclement weather, PM Modi was accorded a red-carpet reception at the Moscow airport. "Cold and rain are no obstacles for a red carpet welcome," tweeted Vikas Swarup, the foreign ministry spokesperson.
Stepping up economic engagement and strategic ties are likely to be the centrepiece of the 16th India-Russia annual summit talks, which will be held between PM Modi and President Putin on Thursday. The talks have been taking place alternately in Moscow and New Delhi since 2000.
A number of pacts in defence and nuclear energy sectors are also likely to be finalised. Russia has been India's biggest supplier of arms, though New Delhi has started buying more military hardware from the US over the last few years.
In the evening, PM Modi will address about 3,000 members of the Indian community at Moscow's Expocentre.
Expanding economic ties is a key agenda, with CEOs from both sides holding a meeting. Currently bilateral trade stands at $10 billion, which the two countries want to enhance to $30 billion in the next 10 years.
On Tuesday, PM Modi chaired a meeting of the Cabinet Committee on Security which is understood to have cleared at least two deals that are likely to be signed during the trip. Russia and India will jointly manufacture 200 Kamov-226T helicopters, in what is seen as a first big step for PM Modi's "Make in India" push in the defence sector.
Defence Ministry sources had said India is also looking at the possibility of leasing a second nuclear submarine from Russia. Last week, the Ministry cleared the purchase of Russian S-400 Triumf air defence missile systems at an estimated cost of Rs 40,000 crore.
Also, India, the third largest oil importer after the US and China, has been pushing for greater involvement in major gas and oil exploration projects in Russia. Russia is one of the top oil producers globally and has huge reserves of natural gas.
PM Modi and President Putin will also discuss the situation in Syria and ways to tackle terrorism. "This would definitely be one of the most important engagements for us," Foreign Secretary S Jaishankar had said.