More than 680 candidates had registered to take part in the presidential election as of Saturday, when the formal registration period ended. The 12-member Guardian Council started the vetting procedure Monday.
Rahimi said Monday he was pulling out of the race, however, because of "heavy executive responsibilities."
"I felt that spending time and energy on the race would hinder the continuity of providing services (to the people)," he was quoted by state-funded broadcaster Press TV as saying.
The Guardian Council said it would take about a week to go through the final list of candidates. Any Iranian national with political or clerical credentials can register to take part in the race, through qualifications must be vetted by the clerical council.
Iranian President Mahmoud Ahmadinejad is ineligible run seek a third term as president because of term limits. Elections are scheduled for June 14.