Voters will elect the 86-seat Assembly of Experts, which enjoys broad powers, including the right to appoint and dismiss ayatollahs, the Islamic Republic's supreme authority figures. The current supreme leader is Ayatollah Ali Khamenei, 67.
More than 160 candidates are taking part in the assembly race, dominated by former President Akbar Hashemi Rafsanjani and Ayatollah Mohammad Taqi Mesbah-Yazdi, known as a spiritual mentor of the incumbent president, Mahmoud Ahmadinejad.
Some 233,000 candidates are running for 113,000 posts in city and town councils, vested with the right to approve community budgets, plan projects, and elect or nominate mayors.
The two main rival groups challenging each other in the council polls are Ahmadinejad loyalists and backers of Tehran Mayor Mohammad Baqer Qalibaf, supported by the country's clergy and neo-conservatives.
The current council race is Iran's third ever, since a reform introduced by ex-President Mohammad Khatami in 1999.
Preliminary results are expected late Sunday or Monday.
