"Based on news we have received, Sayyad Hassan Khomeini's qualification for candidacy for the Assembly of Experts has once again not been approved by the Guardian Council," he wrote on instant messaging service Telegram.
The Guardian Council, a conservative-dominated committee that decides who can run for public office, has barred hundreds of candidates from standing for the assembly on February 26, the same day as parliamentary polls.
The Assembly of Experts monitors the work of Iran's supreme leader, Ayatollah Ali Khamenei, and its 88 members may also be responsible for picking the 76-year-old's eventual successor.
Khomeini, a cleric who has ties to reformist politicians, said last month he would appeal a Guardian Council decision to ban him from running.
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"It's a surprise to me and to many others that some of the honourable gentlemen in the Guardian Council couldn't establish I am qualified," Khomeini had said.
The 43-year-old, the grandson of Ayatollah Ruhollah Khomeini who led the 1979 Islamic revolution that ended the reign of US-backed Shah Mohammad Reza Pahlavi, holds no official political position.
The individuals were not named but a final candidate list is expected on February 16.
The number of people allowed to contest the parliamentary election now stands at 6,185 -- 51 percent of original applicants -- including 586 women.