Black flags flew outside the vast Mosalla mosque, while high-ranking officials including city mayor Bagher Ghalibaf joined the emotional funeral procession.
The 15-storey Plasco building, home to a shopping centre and hundreds of clothing suppliers, collapsed two weeks ago while emergency services were still evacuating people from a huge fire.
The bodies of four civilians have also been pulled from the debris, and six more are missing.
The 16 firefighters were to be buried in the "martyrs" section of a south Tehran cemetery.
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One tearful onlooker, 27-year-old Tahereh Sheydayi, said: "They gave their lives for us. We see it as our duty to attend."
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.
The owners and city officials have been criticised for failing to prevent the disaster at the building, which according to the fire brigade was known to breach multiple safety regulations.
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