"On 'Day of Russia' my good wishes to the people of Russia," he tweeted in English as well as in Russian language.
"I convey my greetings and good wishes on occasion of 'Day of Russia'. India and Russia enjoy unique and time-tested relations, characterised by strong goodwill between our people," Modi said.
He added that it was his "firm belief that special and privileged strategic partnership between our nations will acquire greater relevance in the days ahead."
During the visit, he is expected to hold bilateral talks with Russian President Vladimir Putin.