The 15-storey Plasco building toppled on January 19 while emergency services were still evacuating people from it, four hours into the inferno.
Amir Mahdiani, a fire department commander, addressed worshippers at Friday prayers in Tehran's vast Mosalla mosque as the search for those still missing in the collapse neared its end.
"If it wasn't for the sacrifice of the firemen, maybe the building would have collapsed two hours earlier and hundreds would be buried," he said, before bursting into tears.
Mahdiani said the death toll could have been lower if people had cooperated with the authorities and left the building more promptly.
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He urged the government to help import modern firefighting equipment.
The Plasco building was Iran's oldest high-rise and contained a shopping centre and hundreds of clothes shops and workshops.
The disaster sent a shockwave across Iran, topping the news agenda for a week as rescue teams worked round the clock to recover bodies from the rubble.
Fire and smoke persisted at the site for days as bulldozers unearthed metal rods still red with heat.
Bulldozers had removed 1,600 truckfuls of rubble from the site by today reaching underground floors after nine days of searching with sniffer dogs.
Some of the bodies recovered were unidentifiable and awaited DNA testing.
Authorities said the firefighters would be buried as "martyrs" next to those killed in a stampede during the 2015 hajj pilgrimage.
The last body was recovered late yesterday and officials hoped to clean up and lift traffic restrictions near the site by tomorrow.
The damage was estimated at 15,000 billion rials (USD 390 million, 365 million euros) and some 3,500 workers lost their jobs as a result of the blaze.
The government announced a relief programme to help businesses and uninsured workers.