They added many more people are unaccounted for.
The eight-story building in Savar buckled early Wednesday, reportedly after developing cracks the previous day, authorities said.
The Bangladesh Daily Star reported Wednesday there are estimates as many as 1,600 people might be trapped in the rubble.
Only the ground floor of the building remained standing in one of the worst such disasters in the country, the Daily Star said.
It has not been determined how many people were in the Rana Plaza building -- which housed an indoor market, clothing factories and a bank -- when it collapsed. Teams from the army, border service and fire service had been working around the clock to find survivors, the BBC reported Thursday.
"Many more people, dead or alive, are still trapped inside," Brig. Gen. Ali Ahmed Khan, head of the fire service, told reporters, the Bangladesh Sangbad Sangstha news agency reported.
A manager of the one of the clothing factories on the sixth floor of the building, who was rescued, said his company alone had 450 employees, the Daily Star said.
"We are going to bore holes through the roof and go inside," said Brig. Gen. Mohammad Siddiqul Alam Sikder, who is supervising the rescue operation. "We have to be extremely careful."
The Daily Star said oxygen cylinders were taken to the site to supply fresh air into the holes and crevices.
A similar building collapse in Bangladesh in April 2005 killed 64 workers. Last November, fire engulfed a clothing factory in Dhaka, killing at least 110 people.