"Out of more than 12,000 registered candidates, 4,700 -- or about 40 percent -- were approved," Siamak Rah-Peyk, a spokesman for the Central Elections Supervising Committee was quoted as saying by state television.
The committee is dependent on the Guardian Council, a panel of conservative clerics and jurists, to vet registered candidates and oversee the elections.
Reformist parties have protested against the rejections.
"Out of over 3,000 reformist candidates across the country, only 30 have been approved -- only one percent," Hossein Marashi, an official from the reformist camp, was quoted as saying in the Shaugh daily.
The capital has 30 representatives in Iran's 290-member parliament.
"We are supposed to present a list of 30 candidates," Marashi said. "How are we supposed to do that with just four names?"
The Reformists' High Council for Elections on Monday called for the Guardian Council to revise its decision and asked President Hassan Rouhani to intervene.
"We are concerned that such a trend of extensive rejections of reformist and pro-government candidates might lead to people's reduced participation in the elections," it said in a statement, according to the official IRNA news agency.
Rouhani said Sunday that he would "use his powers as president" to try to change the opinion of the Guardian Council.
The ISNA news agency Monday quoted Elham Aminzadeh, the vice president for legal affairs, as saying Rouhani would "negotiate" with the Guardian Council "to defend the rights of the rejected (candidates) in case mistakes were made".