But local Tehran newspapers and semi-official news agencies reported unofficial results on Saturday showing no single party would be able to claim outright victory, partly because of the divisions within the conservative faction.
There are about 46.5 million eligible voters in Iran and they will choose from 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.
The semi-official Mehr news agency said unofficial results showed that candidates who support Ahmadinejad were trailing Qalibaf.
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 official Islamic Republic News Agency said on Saturday that Rafsanjani was leading in the contest.
Mohsen Esmaili, a candidate running for the Assembly of Experts, told Al Jazeera: "The Expert Assembly is the symbol of connection between the people and the leadership. It has to provide more communication to narrow the gap between the people and their leader."
|The vote is expected to show to what extent|
the reformist have regained popularity
The Assembly of Experts is an 86-member council mandated to appoint and supervise Iran's supreme leader and could become a battleground between conservatives and reformists for control of the government.
Despite its powers, however, the assembly has traditionally kept a low profile and its members are not known to have challenged Khamenei's actions.
Nasser Hadian, a professor at Tehran University, said: "If the reformists win, it is going to be perceived as the beginning of the end - the end of what I would call our 'neo-cons' [neo-conservatives]."
One voter in a working-class neighbourhood of south Tehran said: "He [Ahmadinejad] has listened to the young, defended our nuclear rights, and travelled to the provinces to solve people's problems there directly."
Ahmadinejad himself waited in line for about half an hour to cast his vote at a mosque in east Tehran.
Western powers have been alarmed by his anti-Western and anti-Israel statements and many are concerned that Iran may be attempting to develop nuclear weapons.
John Bolton, outgoing US ambassador to the UN, recently said in New York that the UN should charge Ahmadinejad with inciting genocide.
Bolton called Ahmadinejad's words and actions "outrageous" and "unacceptable".