The elections, held on Friday, are the first test of Mahmoud Ahmadinejad, Iran's president, at the polls since he was elected in June 2005.
Ahmadinejad said on state TV: "I am sure that our people will once more show off their greatness to the people of the world by participating in the election."
Ayatollah Ali Khamenei, Iran's supreme leader, urged Iranians to "prove to the world Iran's honour in another revolutionary challenge".
Güncelleme Tarihi: 20 Eylül 2018, 18:16
Iran's reform movement was defeated in municipal elections in 2003, and later in parliamentary and presidential elections, by Ahmadinejad and his conservative allies.
Friday's elections are expected to show to what extend the reformists have regained popularity.
Voter turnout during the 2003 polls was the lowest recorded election participation in the Islamic republic's history.
There are about 46.5 million eligible voters in Iran and they will choose between approximately 233,000 candidates for more than 113,000 city and rural council posts.
While the reformists hold no seats on the Tehran City council, the conservatives are split between supporters of Ahmadinejad and his rival Mohammad Baqer Qalibaf, now the mayor of Tehran.
In the Assembly of Experts election, the race is seen to be between Akbar Hashemi Rafsanjani, a cleric and former president, and Ayatollah Mohammad Taqi Mesbah-Yazdi, a theologian regarded by many as Ahmadinejad's mentor.
The Assembly of Experts is an 86-member council mandated to appoint and supervise Iran's supreme leader.
Despite its powers, the assembly has traditionally kept a low profile and its members are not known to have challenged Khamenei's actions.
Polling stations open at 9am (05:30 GMT) but results are not expected until late on Sunday.