He faces stiff competition from hardline cleric Ebrahim Raisi, 56, who has positioned himself as a defender of the poor and called for a much tougher line with the West.
Supreme leader Ayatollah Ali Khamenei cast his ballot just minutes after polls opened at 8:00 am (0330 GMT).
"The destiny of the country is in the hand of Iranians," he told reporters as he voted in Tehran.
Long lines had already formed at polling stations in the capital.
Rouhani has pushed the boundaries over the past fortnight, criticising the continued arrest of reformist leaders and activists, and calling on security agencies not to interfere in the vote.
Raisi says he will stick by the 2015 nuclear deal with world powers, that saw curbs to Iran's atomic programme in exchange for sanctions relief, but he points to the continued economic slump as proof that Rouhani's diplomatic efforts have failed.
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