The blast occurred just before 11:00pm (0100 EST), 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.
"We are not ruling out the possibility that they might be responsible for this but it is too early to speculate."
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.
Duterte was in Davao on Friday but was not near the market when the explosion occurred, according to his aides.
They said he went straight into meetings with security chiefs following the blast.
Violence-plagued region
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.
Duterte became well known for bringing relative peace and order to Davao with hardline security policies, while also brokering local deals with Muslim and communist rebels.
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.
Abu Sayyaf threat
However Duterte also ordered a military offensive to eliminate the Abu Sayyaf, a small but extremely dangerous group of militants that has declared allegiance to Islamic State and vowed to continue fighting.
Fifteen soldiers died on Monday in clashes with the Abu Sayyaf on Jolo island, one of the Abu Sayyaf's main strongholds about 900 kilometres from Davao.
Presidential spokesman Andanar referred to the fighting on Jolo when he speculated on who may have been behind Friday's bomb attack.
The Abu Sayyaf claimed responsibility for three bomb attacks in 2005 -- one in Davao, one in a nearby city and a third in Manila -- that killed eight people.
The Abu Sayyaf, notorious for kidnapping foreigners to extract ransoms, said it conducted the 2005 attacks in response to an offensive against it at that time.
Andanar on Friday also raised the possibility of drug lords carrying out the attack as a way of fighting back against Duterte's war on crime.
Duterte has made eradicating illegal drugs the top priority of the beginning of his presidency.
Security forces have conducted raids in communities throughout the country to arrest or kill drug traffickers.
More than 2,000 people have died in the war on crime.
The United States, the United Nations and rights groups have expressed concern about an apparent wave of extrajudicial killings.
But the United States quickly released a statement expressing deep condolences for Friday's blast.
