Putin, who has ruled Russian Federation for nearly two decades, recorded his best ever election performance with 76.67 percent of the vote but rejected the possibility of staying in power indefinitely.
"Conveying his compliments on Putin's success, the Prime Minister expressed the hope that under Putin's leadership, the Special and Privileged Strategic Partnership between India and the Russian Federation will continue to grow from strength to strength", the Prime Minister's Office said in a statement.
None of the seven candidates who ran against Putin posed a threat, and opposition leader Alexei Navalny was barred from running. "What, do you think I will sit (in power) until I'm 100 years old?" he said, calling the question "funny".
Spokesman for Putin's campaign Andrei Kondrashov said that at more than 67 percent, turnout was 8 to 10 percentage points higher than expected.
According to the chairman of the Russian Central Election Commission, 73.37 million people voted in the elections.
"Our people always unite in the trying hour".
Putin secured 74 percent of presidential votes polled according to a state-run exit poll.
Most of the voters AFP spoke to said they had backed Putin despite Russia's problems of poverty and poor healthcare, praising his foreign policies.
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At odds with the West over Syria, Ukraine, allegations of Russian election meddling and cyber-attacks and the poisoning in Britain of a former Russian spy and his daughter, relations between Moscow and the West are at a post-Cold War low.
Authorities also used both the carrot and the stick to boost engagement in the polls.
Selfie competitions, giveaways, food festivals and children's entertainers were laid on at polling stations to entice voters. But employees of state and private companies, as well as students, reported coming under pressure to vote.
In his next six years in office, Putin is likely to assert Russia's power overseas even more strongly.
Russian presidential elections were as open as possible, Pamfilova said. "A regular meeting of the top-level Cooperation Council scheduled for early April will contribute to that", the Kremlin said.
Runner-up Grudinin said the elections had been "dishonest".
He had urged supporters to boycott the "fake" vote and sent out more than 33,000 observers to see how official turnout figures differed from those of monitors. With leading rival Aleskei Navalny kept out, the election was a formality. This was more a referendum than a serious choice of candidates.