"Because of the rush of voters, voting will be extended for sure," beyond the scheduled close of 6 pm (1330 GMT), he said, quoted by Fars news agency.
Iran is electing a successor to President Mahmoud Ahmadinejad, who after serving two consecutive terms is constitutionally barred from running.
The voting was taking, according to the Guardians Council electoral watchdog, "without any problems."
The interior ministry has not given turnout figures. State television also broadcast footage of long queues at polling stations across the country where more than 50 million people are eligible to vote.