"Our colleagues in the fire department have lost their lives while trying to save the people in the fire," Mohammad Baqer Ghalibaf told the Islamic Republic of Iran News Network.
Earlier Thursday, Tehran's fire department spokesman Jalal Maleki told IRINN an estimated 20 to 30 firefighters were on the third floor of the high-rise Plasco building when it collapsed.
Maleki also told a local journalist at the scene that 35 firefighters were missing and that rescue workers were trying to dig them out.
The cause of the building fire and collapse is being investigated, he added.
The journalist on the scene, who spoke to CNN but declined to be named, said police and other uniformed security personnel have blocked the area and are not allowing people or cars to enter.
The journalist said that when he got there, several firefighters were inside the collapsed building and were feverishly trying to clear the debris and find buried colleagues, but their commander, using a loud speaker, had ordered them all out before assigning them to specific tasks.
Iran's semi-official Fars news agency reported that the Plasco building -- a downtown commercial garment building and one of Tehran's oldest high-rises -- "no longer exists."
Official news agency IRNA cited the head of Tehran Emergency Services as saying 70 people had been injured in the fire.
A spokesman for Tehran Emergency Services, Hassan Abbasi, told IRNA that 23 seriously injured people were receiving hospital treatment. The remaining 47 had minor injuries and were treated at the site, Abbasi said.
Report: 70 injured
Fars cited Maleki as saying that some 10 fire departments responded immediately to the blaze. But, he added, some people didn't realize the building was on fire because Tehran's air pollution masked the smoke from the blaze.
Maleki also reportedly said the fire is now out, but rescue operations are in full swing.
"The building collapsed on itself (vertically) and did not damage the adjacent buildings," IRNA quoted Maleki as saying.
IRNA said staff members at two nearby embassies and residents of many surrounding buildings had been asked to leave as a precaution.
The agency quoted Tehran Governor Hossein Hashemi as saying the fire was an accident and that no security issue was involved.
Fars cited Mojtaba Doroodian, head of the shirt makers' union, as saying that the fire was the result of a leak in a small gas cylinder on the 10th floor, which caused an explosion when a merchant turned on the lights in his store.
"When people in the building became aware of the fire they tried to put it out with fire extinguishers, but the fire extinguishers were empty," Doroodian is quoted as saying.
The fire blazed through the upper stories for over three hours, sending out thick plumes of black smoke, before the building came down.
The Plasco building, built more than 50 years ago, was home to hundreds of garment manufacturers and other businesses, Fars reported. Most were evacuated, it said.
Located on Jomhouri Avenue in central Tehran, the Plasco building was constructed in 1962. It was named after a successful plastics business, Plascokar.
Seventeen stories tall, it was the country's first private high-rise building and soon became a well-known feature of the city's skyline.
Alistair Esfahanizadeh, who took a picture of the building before the collapse, posted on his Instagram account Thursday: "I probably took one of the last pictures of the building standing yesterday before the sunset."
The building housed offices and shops. The Plasco Shopping Center, known mostly for its clothing stores, was spread across several floors.