The SITE Intelligence Group, which monitors ISIS' online activity, said the militants claimed responsibility via their Amaq propaganda agency.
The deaths included 15 civilians and five troops. Among the wounded were 17 troops, two police, two coast guard and 90 civilians.
Troops in armored carriers sealed off the main road leading to the church while vehicles transported the dead and wounded to the town hospital. Some casualties were evacuated by air to nearby Zamboanga city.
"I have directed our troops to heighten their alert level, secure all places of worships and public places at once, and initiate pro-active security measures to thwart hostile plans," Defense Secretary Delfin Lorenzana said.
"We will pursue to the ends of the earth the ruthless perpetrators behind this dastardly crime until every killer is brought to justice and put behind bars. The law will give them no mercy," the office of President Rodrigo Duterte said in Manila.
It added that "the enemies of the state boldly challenged the government's capability to secure the safety of citizens in that region. The (Armed Forces of the Philippines) will rise to the challenge and crush these godless criminals."
Witnesses said the first blast inside the Cathedral of Our Lady of Mount Carmel in Jolo, Sulu province, sent churchgoers, some of them wounded, to run out of the main door. Army troops and police posted outside were rushing in when the second bomb exploded about one minute later near the main entrance, causing more deaths and injuries. The military was checking a report that the second explosive device may have been attached to a parked motorcycle.
The initial explosion scattered the wooden pews inside the main hall and blasted window glass panels, and the second bomb hurled human remains and debris across a town square fronting the cathedral.
The attack came nearly a week after minority Muslims in the predominantly Roman Catholic nation endorsed a new autonomous region in the southern Philippines in hopes of ending nearly five decades of a separatist rebellion that has left 150,000 people dead. Although most of the Muslim areas approved the autonomy deal, voters in Sulu province rejected it. The province is home to a rival rebel faction that's opposed to the deal as well as smaller militant cells that not part of any peace process.
Western governments have welcomed the autonomy pact. They worry that small numbers of ISIS-linked militants from the Middle East and Southeast Asia could forge an alliance with Filipino insurgents and turn the south into a breeding ground for extremists.
The Associated Press contributed to this report.