A Bureau of Fire Protection commander at the scene said the chances of the 37 surviving were "zero", Paolo Duterte, the vice mayor, who is also the president's son, wrote in a Facebook post.
The blaze started at the four-storey NCCC Mall on Saturday morning and people were trapped inside, including in a call centre on the top floor, Ralph Canoy, a police officer in the district, told AFP.
Canoy said the fire was still going before dawn on Sunday morning.
"The fire started on the third floor, which houses products like fabrics, wooden furniture and plastic ware, so the fire quickly spread and it's taking a long time to put out," he said.
He said investigators believed some of those likely killed had been trapped in the call centre, which operated 24 hours a day.
President Rodrigo Duterte, who served as mayor of Davao for about two decades and continues to live in the city, visited the mall on Saturday night to comfort relatives of the victims, one of his aides told AFP.
Davao is the biggest city in the southern Philippines. It is about 1,000 kilometres (600 miles) south of Manila.
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