"Everyone should vote in this important election. vote at early hours", Supreme Leader Ayatollah Ali Khamenei said after casting his vote in the capital Tehran.
With nearly all votes counted, Rouhani looked to have an insurmountable lead with 22.8 million votes - or 59 percent - compared to 15.5 million for his hardline challenger Ebrahim Raisi, election committee chief Ali Asghar Ahmadi announced on state television.
Iranian President Hassan Rouhani has been re-elected, state television has declared.
More than a third of Iran's 80 million population is under age 30 and yearns for reform.
The crowning achievement of Rouhani's first term was a deal with global powers to curb Iran's nuclear programme in return for the lifting of most financial sanctions.
"I voted out of concern that a no-show would benefit Raisi", said Milad, who headed to a polling station in downtown Tehran late Friday.
Counting is underway on Saturday in Iran's Presidential election, with the official turnout said to be at about 70 per cent, poll officials said.
However, Raisi later appeared at the Ministry of Interior in Tehran on Friday and complained of a shortage of ballot sheets at many polling stations, according to Fars.
The 56-year-old Raisi, who heads an influential religious charitable foundation with vast business holdings, is seen by many as close to Khamenei.
Rouhani won 21.6 million votes in Friday's hard-fought contest, compared to 14 million for Raisi, with 37 million votes counted, the source said, adding about four million more votes were still to be tallied.
Iran?s Foreign Minister Mohammad Javad Zarif, has applauded the massive voter turnout for the presidential election. Another report, however, said the deadline had been extended by five hours.
Before the victory of the Islamic Revolution in 1979, President Rouhani used to preach against the Shah (the toppled king of Iran), and had to change his name to avoid detection by the secret services. But he remains subordinate to the supreme leader, who is chosen by a clerical panel and has the ultimate say over all matters of state. Raisi ran a populist campaign, vowing to fight corruption and fix the economy while boosting welfare payments to the poor.
Hashemitaba was among the first to predict an outright win for Rouhani as he offered his congratulations Saturday morning.
But analysts agreed the gathering of Khamenei's powerful allies behind Raisi seemed to have the unintended effect of energising Rouhani's supporters, uniting opposition and pro-reform figures, artists and activists to back his re-election.
All candidates for elected office must be vetted, a process that excludes anyone calling for radical change, along with most reformists. Rouhani has been unable to secure the release of reformist leaders from house arrest, and media are barred from publishing the words or images of his reformist predecessor Khatami.