The attack was carried out in a university gymnasium in Marawi, a city in the south of the country besieged by Islamist militants for five months in 2017.
The Islamic State group, which wields influence in the country's south, said on Telegram its members had detonated the bomb.
Earlier on Sunday, before Islamic State's claim, Philippine President Ferdinand Marcos Jr condemned "the senseless and most heinous acts perpetrated by foreign terrorists".
Police and the military strengthened security in the country's south and around the capital Manila.
In Rome, Pope Francis offered prayers for the victims during his Sunday address and, in a separate written message, appealed to "Christ the prince of peace (to) grant to all the strength to turn from violence and overcome every evil with good".
Law enforcement operations to bring to justice the perpetrators of the "terrorist activity" will "continue unabated," Defence Secretary Gilberto Teodoro told a press conference.
There were "strong indications of a foreign element" in the bombing, Teodoro said, refusing to elaborate so as not to compromise ongoing investigation.
Fragments of a 16-mm mortar were recovered at the scene, senior police official Emmanuel Peralta told the press conference.
The blast in Marawi, capital of Lanao del Sur province, followed a series of military operations against local pro-Islamic State groups in the southern Philippines, the military chief said.
Muslims gathered in solidarity with the victims of a deadly bomb attack in Mindanao. (EPA PHOTO)
One on Sunday in Lanao del Sur led to the killing of a leader of the Dawlah Islamiya-Maute group.
"It is possible that what happened this morning was a retaliatory attack," Armed Forces Chief Romeo Brawner told the press conference.
The Islamic State-linked Maute seized Marawi on May 2017, seeking to make it a Southeast Asian "wilayat" – or governorate - for Islamic State.
In the ensuing five-month battle, Islamist fighters and Philippine forces killed more than a thousand people, including civilians.
Images shared by the Lanao del Sur government on Facebook showed military officials surveying the gym at the Mindanao State University where the blast occurred, which appeared intact except for burn marks in the centre.
Videos posted by DZBB radio on social media platform X showed rescuers carrying injured people out of the gym on plastic chairs.
Police offices in Mindanao and the capital region were placed on high alert and police checkpoints tightened "to prevent possible follow-up incidents", police official Peralta said.
The coast guard directed its districts to intensify pre-departure inspections at ports.
Muslims gathered in solidarity with the victims of the bomb attack in Mindanao on Sunday, saying they condemned the attack.
Mindanao State University said in a Facebook post it was "deeply saddened and appalled by the act of violence that occurred during a religious gathering".
"We unequivocally condemn in the strongest possible terms this senseless and horrific act."
The university said it was suspending classes until further notice.
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