The blast occurred just before 11:00pm (1500 GMT) yesterday, leaving bodies strewn amid the wreckage of plastic tables and chairs on a road that had been closed to traffic for the market in the heart of Davao city.
An improvised explosive device caused the explosion, presidential spokesman Martin Andanar said, adding drug traffickers opposed to Duterte's war on crime or Islamic militants may have been responsible.
"There are many elements who are angry at our president and our government," Andanar told DZMM radio, after referring to the drug traffickers and the militants.
Twelve people were confirmed killed and more than 30 others injured, according to Ernesto Abella, another presidential spokesman.
Davao is the biggest city in the southern Philippines, with a population of about two million people. It is about 1,500 kilometres (930 miles) from the capital of Manila.
The blast occurred in the centre of Davao, close to one of the city's top hotels that Duterte sometimes holds meetings in, as well as a major university.
"The force just hurled me. I practically flew in the air," Adrian Abilanosa, who said his cousin was among those killed, told AFP shortly afterwards.
They said he went straight into meetings with security chiefs following the blast.
Davao is part of the southern region of Mindanao, where Islamic militants have waged a decades-long separatist insurgency that has claimed more than 120,000 lives.
Communist rebels, who have been waging an armed struggle since 1968, also maintain a presence in rural areas neighbouring Davao.
Duterte had been mayor of Davao for most of the past two decades, before winning national elections in a landslide this year and being sworn in as president on June 30.
However in 2003, two bomb attacks blamed on Muslim rebels at Davao's airport and the city's port within a month of each other killed about 40 people.
Duterte has in recent weeks pursued peace talks with the two main Muslim rebel groups. Its leaders have said they want to broker a lasting peace.
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