Rescue workers, soldiers and sniffer dogs were desperately hunting for survivors in the debris of the 15-storey Plasco building, which contained a shopping centre and hundreds of clothing suppliers.
There was no official confirmed death toll several hours after the collapse.
The capital's mayor, Mohammad Bagher Ghalibaf, rowed back on an earlier statement that "more than 20" firefighters were known to have died.
"Around 20 of my colleagues in the fire brigade managed to save people but went back to make sure nobody is inside," he told state television.
"Before they managed to get to the lower floors, the building collapsed and some of my colleagues were martyred."
Fire brigade spokesman Jalal Maleki said: "About 20 are under the rubble for sure, and definitely some have been martyred."
Dramatic images showed flames pouring out of the top floors of the 55-year-old building, which then collapsed live on television after a four-hour blaze.
The fire was initially contained but was then reignited by an explosion on the 10th floor, fatally weakening the building's steel structure, Ghalibaf said.
A Red Crescent aid official said 13 teams of sniffer dogs and four robot search devices were working at the scene.
A tunnel had been dug from an adjacent car park to reach the basement of the building where survivors may still be trapped, a city councillor told the ISNA news agency.
President Hassan Rouhani said the "nation of Iran mourns and praises those sacrificing firefighters", and he asked citizens to pray for their families and the injured.
Condolences
Condolences came from around the world, with the London Fire Brigade tweeting: "Our thoughts are with the friends and families of the firefighters who have died" in Tehran.
Some 78 people -- mostly firefighters -- were injured during the initial stages, the head of Tehran's emergency services told state television, and six were still in hospital by late evening.
"I was inside and suddenly I felt the building is shaking and is about to collapse. As we gathered colleagues and got out, a minute later the building collapsed," said Ali, a firefighter at the scene.
Local media said the workshops were especially full of clothes in the build-up to Nowruz, the Iranian New Year which falls in March.
Rouhani demanded an immediate investigation.
"More than 30 times we warned the building's owners that it was not safe, but unfortunately they did not pay attention," said municipality spokesman Shahram Gilabadi.
The fire brigade spokesman said the building was known to breach safety standards.
"Even in the stairwells, a lot of clothing is stored and this is against safety standards. The managers didn't pay attention to the warnings," Maleki told state television, adding that the building lacked sufficient fire extinguishers.
'Preparing for New Year'
Dozens of Tehranis queued to donate blood, with one young man telling state television: "This is the least we could do for those who take their lives into their hands to rescue others."
Tehran's tailors' union said there were around 400 clothing suppliers inside. "They were preparing clothing for the New Year and that's why all supply units were full of clothes," its head said.
The Plasco building was Tehran's first shopping centre and Iran's tallest building when it was finished in 1962, before being dwarfed by the construction boom of later years.
It was built by Habibollah Elghanian, a prominent Iranian-Jewish businessman who was arrested for ties to Israel and sentenced to death and executed after the 1979 Islamic revolution.
