Hadi Tahan Nazif said the vetting body is checking the candidates’ qualification and the voting in the 12-membner council will be carried out through secret ballots.
Iran’s interior ministry said 80 people filed for candidacy within the five-day registration period that ended on Monday.
Iranian Parliament Speaker Mohammad Baqer Qalibaf, former parliament speaker Ali Larijani and former first vice-president Eshaq Jahangiri, former president Mahmoud Ahmadinejad, and former presidential candidate Saeed Jalili are among the main contenders.
Larijani and Ahmadinejad have formerly been disqualified to stand for elections, but Nazif explained the qualification of candidates is vetted independently of the results in previous elections.
Political analysts speculate in case Larijani is qualified, he has high chances of winning the snap polls.
Reformists have announced they will not support any stalking horse and will field real candidates.
Iranians will cast their ballots on June 28 to choose a successor for the late President Ebrahim Raisi, who died along with his accompanying delegation in a helicopter crash on May 19.