Duterte's special assistant Christopher Go confirmed the bulk of the conversation to AFP.
Officials said numerous people trapped inside worked at a call center located in the mall. Our firemen are still struggling to find a way in as the fire is still burning.
Flames were eventually brought under control early on Sunday morning but fire officials said they had not yet entered the section where they believed the missing were trapped.
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"I am also praying for the safety of the missing persons in the mall fire", she told them, adding that she would do anything she could to assist.
Duterte's daughter Davao City Mayor Sara Duterte said Sunday the body of one of the victims has been retrieved.
The fire broke out around 9:30 a.m., (0030GMT) razing the mall that would have extended operating hours to customers preparing for Christmas Eve, according to Davao City-based local media.
The blaze started at a furniture store on the third floor and quickly spread to the next level.
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It was not immediately known if the six people rescued were call centre workers, mall employees or shoppers.
"The fire hasn't totally been put out", Romina Marasigan, spokeswoman of the government's disaster-response agency, said.
"We are now coordinating with the authorities", said Thea Septaan Padua, a spokeswoman for the mall.
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