The building, "Rana Plaza", collapsed around 8:45 a.m. Wednesday and since then rescuers have been trying to extricate those still buried under the debris.
Relatives of the missing said scores of people were still unaccounted for.
In one of the worst building collapses ever in Bangladesh, officials said rescuers have so far pulled out alive more than 2,000 people, including 41 early Friday.
"The death toll from the building collapse has climbed to 271," Wali Ashraf, a police official, told Xinhua Friday.
He said 41 trapped people were rescued alive from beneath the rubble of the eight-storeyed building early Friday, keeping alive the hope that more lives can be saved as the rescue operation continues.
Of the bodies, he said 223 have so far been handed over to their relatives.
Rescuers with support of hundreds of volunteers and locals worked frantically through the second consecutive night to rescue those trapped in the rubble.
They say the salvage operations at the site will continue until Saturday before the process to remove the rubble begins.
Apart from a bank's branch and many shops, the building housed five garment factories which, according to garment manufacturers' association, employed nearly 3,500 workers, mostly women.