The two leaders met for 40 minutes on the sidelines of the BRICS summit here late last night after their Monday meeting was deferred because of Putin's engagements in Brazil's capital Brasilia.
"Talked about strengthening Russia-India ties in my meeting with President Putin. We value our friendship with Russia," Modi tweeted after his meeting with Putin as the Prime Minister.
Putin congratulated Modi on his great victory in the recent elections.
Modi, who has met Putin in 2001 in Moscow, said that India's ties with Russia is a time-tested relationship and he appreciates that it has been so since early independence.
He expressed deep appreciation for Russia's friendship and unstinting bilateral and international support for India's economic development and security since India's independence.
Speaking in Hindi, he remarked, "Even a child in India if asked to say who is India's best friend will reply it is Russia because Russia has been with India in times of crisis."
"The Prime Minister conveyed his sincere appreciation and admiration for President Putin's decisive leadership in deepening and expanding the India-Russia special and privileged strategic partnership," said a statement issued by the Prime Minister's Office.
He said India is committed to taking the relationship forward and the focus is to broaden the strategic partnership including in the areas of defence, nuclear energy, space, energy, trade and investment, people-to-people contacts and addressing regional and global challenges.
The prime minister said there was need to look at a liberal visa regime, especially students going for studies.
President Putin acknowledged that there was a case for looking at it, MEA spokesman Syed Akbaruddin said.
Modi suggested that President Putin should travel outside Delhi when he comes for the annual summit dialogue in December and visit a nuclear construction site, an apparent reference to the Kudankulam II project.
Putin responded saying "it is a good idea".
Units 1 and 2 of Tamil Nadu-based Kudankulam Nuclear Power Plant (KKNPP) have been built with the help of Russian assistance at the cost of Rs 17,200 crore.
India and Russia signed a General Framework Agreement on unit 3 and 4 in April this year after crossing the initial hurdles of the Civil Liability Nuclear Damage Act 2010.
Modi fondly recalled his visit to Russia's Astrakan region in his early days as Chief Minister of Gujarat which has ties with that region. Talking about that visit, he said he felt as if he was in India.
Putin said Russia places its relations with India high enough in the strategic framework. Nuclear power project has been a symbol of India-Russia relations.
Modi appreciated Putin's speech at the BRICS summit saying it was clear on issues like reforms of the UN security council and international financial organisations.
The two leaders looked forward to their Annual Summit in Delhi in December 2014 as an opportunity to outline a bold vision and roadmap for their relationship in the years ahead.