"I am sure that during your new term, relations between our two countries will develop further," he said in a message on the presidential website.
Russia votes with strongman Putin set for fourth term
Rouhani emphasised "the will and determination of the Islamic Republic of Iran to strengthen its cooperation with Russia bilaterally, regionally and internationally".
Vladimir Putin is set for another six years in power after winning a record victory on Sunday.
Putin cruises to landslide election win
Putin, who has ruled Russia for almost two decades, recorded his best ever election performance with 76.67 percent of the vote, but rejected the possibility of staying in power indefinitely.
Iran and Russia have strengthened their ties in recent years, both giving major military and financial backing to Syrian President Bashar al-Assad.
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