Confirming that the second round would be held on Friday, the council also said on Sunday that it was allowing three days for any disgruntled voters or candidates to lodge complaints after one candidate said the vote was rigged.
"The electorate has three days after the first round to complain," an official attached to the Guardians Council, Mohammad Jahromi, told state television. The first round was held on 17 June.
"We hope to finish examining the complaints by Monday, and the candidates will have two days to campaign," council spokesman Gholamhossein Elham told the official Islamic Republic News Agency.
The council, a 12-member body which the constitution charges with protecting the Islamic republic, must formally confirm the result and even has the power to annul the election. The panel also decided who could stand.
None of the seven candidates in the election managed to win more than 50% of the vote, meaning the top two - Tehran's mayor Mahmood Ahmadinejad and cleric Akbar Hashemi Rafsanjani - will go into a run-off.
Former parliament speaker Mehdi Karoubi, who came third, said on Saturday that Ahmadinejad's surprisingly strong show was the result of an elaborate plot to rig the polls.
Iranian election officials can
register complaints until Monday
"Him announcing does not make it a complaint," Elham said. "He has to give his complaint plus proof to the Guardians Council. The complaints should be documented and very clear."
Instead of lodging a complaint, Karoubi appealed to supreme leader Ayatollah Ali Khamenei to "appoint an honest and trusted committee" to investigate the Guardians Council - an unelected political watchdog - as well as the Interior Ministry, the Revolutionary Guards and the hardline Basij militia.
Karoubi said had tapes that implicated Revolutionary Guard commanders, and said some Basij members had been allowed to vote more than once.
"It was not like that," Elham said, also dismissing allegations that Basij members had been employed as polling station supervisors.
"Being a Basiji or not being a Basiji was not a criteria for choosing supervisors. The supervisors were people who had the necessary qualifications to act as supervisors," he said.