A total of 801 people registered to stand for the powerful Assembly of Experts, which monitors the work of supreme leader Ayatollah Ali Khamenei, election headquarters secretary Ali Motlagh told media after registration closed Wednesday.
The reformist candidates include Akbar Hashemi Rafsanjani, who was Iran's president from 1989 to 1997 and is now considered a moderate.
Hassan Khomeini, the 43-year-old grandson of the Islamic Republic of Iran's founder Ayatollah Ruhollah Khomeini, also signed up to take part in the vote, slated to take place on February 26.
Members of the assembly are chosen by the public for a term of eight years from a list that is pre-screened by another powerful committee, the Guardian Council.
Both the Assembly and the Council are considered to be dominated by conservatives.
In theory, the Assembly can dismiss the supreme leader, and would be responsible for picking a replacement. It would have the same task should Khamenei die.
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Sixteen women were among those who signed up to run for the assembly, following a call from moderate President Hassan Rouhani for women to stand in elections.
No woman has sat on the Assembly of Experts since its foundation in 1982.
Rouhani did not specify in which polls he was inviting women to participate.
Parliamentary elections will take place on the same day as those for the assembly.
Former presidential candidate Mohammad Reza Aref -- a senior figure in the reformist camp -- is among those running for parliament.
He helped Rouhani win his 2013 presidential bid by stepping aside in his favour.
Rouhani's recent nuclear deal with world powers could help more moderates and reformists enter the parliament, observers say.
Rouhani has faced vocal opposition from the present parliament, including on the nuclear deal, and a less hostile house would give him a greater chance of passing at least limited social reforms, which he championed in his 2013 election campaign.
So far, 5,359 men and 562 women have registered to run for parliament ahead of a Friday deadline, Motlagh said