The reformist alliance formed in support of moderate President Hassan Rouhani had campaigned against both Yazdi, the outgoing chairman of the Assembly of Experts and Mesbah-Yazdi, an outspoken opponent of the reformists.
Iran’s leader calls for parliament that stands up to the West
But a third conservative, Ahmad Jannati, who had been targeted by the pro-Rouhani coalition, narrowly kept his seat on the assembly, a powerful committee which oversees the work of supreme leader Ayatollah Ali Khamenei, state television reported.
Jannati, who chairs the conservative-dominated Guardian Council which must confirm the results of Friday's elections for both the assembly and for parliament, came 16th in Tehran, and scraped the last of the capital's 16 assembly seats.
Verification of the result is not expected for several days.
Elections in Iran
The election to the 88-member Assembly of Experts is important because it will pick Khamenei's successor if he dies during its eight-year term.
Rouhani placed third in polling for the assembly in Tehran and his key ally, former president Ayatollah Akbar Hashemi Rafsanjani took first place.
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