Deputy Interior Minister Ali Asghar Ahmadi told journalists in a televised news conference that more than 40 million Iranians voted in yesterday's election. That puts turnout above 70 per cent.
Election officials repeatedly extended voting hours until midnight to accommodate long lines of voters, some of whom said they waited hours to cast their ballots.
Yesterday's vote was largely a referendum on Rouhani's more moderate political policies, which paved the way for the landmark 2015 nuclear deal that won Iran relief from some sanctions in exchange for curbs on its nuclear program.
Preliminary vote tallies have him ahead with 14.6 million votes, out of 25.1 million counted so far.
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His nearest challenger is hard-line cleric Ebrahim Raisi, with 10.1 million votes.
The two other candidates left in the race, Mostafa Mirsalim, a former culture minister, and Mostafa Hashemitaba, a pro-reform figure who previously ran for president in 2001, respectively have 297,000 and 139,000 votes each.
Iran's president is the second-most powerful figure within Iran's political system. He is subordinate to the country's supreme leader, who is chosen by a clerical panel and has the ultimate say over all matters of state.
All candidates for elected office must be vetted, a process that excludes anyone calling for radical change, along with most reformists. No woman has ever been approved to run for president.
Ahmadi said the Interior Ministry hopes to have final results later today.