President Rodrigo Duterte, himself a Davao native, visited distraught relatives outside the burning building overnight but told them there was "zero" chance their loved ones had survived, witnesses told AFP.
Firemen found one body as the blaze was finally extinguished Sunday, Davao Mayor Sara Duterte -- the president's daughter -- told reporters.
Firemen have concluded that all those trapped in the building are dead, she said, adding: "They assessed that no one would survive in that heat and with that thick, black smoke."
The deadly fire adds fresh misery for the mainly Catholic Philippines at Christmas as the death toll from a tropical storm that hit the south of the country Friday crossed 200 and with tens of thousands displaced by severe flooding and landslides.
The blaze started at the four-storey NCCC Mall Saturday morning, sending thick plumes of black smoke billowing into the sky over Davao.
With low wages but strong English language skills, the Philippines is a popular destination for international companies to set up customer call centres.
The building's top floor housed a 24-hour call centre for the US-based market research company SSI.
Jimmy Quimsing, a retired seaman, was one of the relatives desperately waiting for news.
His 25-year-old son Jim Benedict worked at the call centre and had not been in contact since the fire broke out.
Quimsing said he spoke to President Duterte and had been told to prepare for the worst.
"He told us ... no one would survive under these circumstances," he told AFP.
Duterte's special assistant Christopher Go confirmed the bulk of the president's comments to AFP.
Paolo Duterte, the president's son and the vice mayor of Davao, also wrote on Facebook that fire officials had told him there was "zero" chance of anyone trapped surviving the blaze.
- 'No ventilation' -
In a statement on its local Facebook page, SSI said it would set up a "command centre" for the relatives of those missing.
"Please continue to pray for everyone's safety," the firm added.
Davao fire marshal Honeyfritz Alagano said the blaze may have started by a spark on the third floor of the mall, which had a furniture section.
"One of our firemen here has a kid who is (a call centre) agent in there. He told us some of them went to collect their stuff at their lockers and were trapped," Alagano told AFP.
"The mall is an enclosed space with no ventilation. When our firemen tried to enter they were pushed back by smoke and fire."
Mayor Duterte said she told the fire-fighters to retrieve all the dead, stressing: "you do not stop until you find 37."
She also said the circumstances surrounding the fire would be investigated but added that it was too early to say who was at fault.
Deadly blazes occur regularly in the Philippines, particularly in slum areas where there are virtually no fire safety standards.
"It's possible that while they were working, they did not immediately notice the fire spreading," Davao police officer Ralph Canoy told AFP, referring to the call centre workers.
Davao, with a population of about 1.5 million people, is the biggest city in the southern Philippines. It is about 1,000 kilometres (620 miles) south of Manila, the nation's capital.
President Duterte served as mayor of the city for more than two decades and continues to visit on weekends.
His daughter succeeded him when he ran for president, with one of his sons winning the vice mayoralty post.
Most of those killed by the recent tropical storm were also in the southern region of Mindanao.
There have also been horrific fires in bigger buildings and factories, where corruption and exploitation mean supposedly strict standards are often not enforced.
In 2015, a fire tore through a footwear factory in Manila, killing 72. Survivors of that blaze blamed barred windows and other sweatshop conditions for trapping people inside the factory.
In the deadliest fire in the Philippines in recent times, 162 people were killed in a huge blaze that gutted a Manila disco in 1996.//AFP