Tito Karnavian, Indonesia's police chief, said that the suicide attack outside Surabaya's police headquarters in the centre of the city was carried out by a family of five, including an eight-year-old girl, who survived the attack.
Police said the father detonated a auto bomb; the two sons, ages 16 and 18, reportedly used motorcycles rigged to explode; and the mother and two daughters, ages 9 and 12, wore explosives on their bodies, the BBC reported.
On Sunday night, a bomb in the Wonocolo low-priced housing complex in Sidoarjo exploded prematurely, killing a woman and her 17-year-old child, police said.
The wave of attacks began on Sunday with a young family of six bombing three Christian churches on Sunday morning, killing 12 people and injuring at least 40 others.
Gen Karnavian said police recovered unexploded pipe bombs in another incident in Sidoarjo, south of Surabaya, in an apartment where an explosion killed three members of a family alleged to have been making bombs.
The reflection of a church struck by suicide bombers is seen in Surabaya, Indonesia, May 14. At least seven others were killed in the blasts.
Joko Widodo, Indonesia's president condemned the latest bombing, calling it "cowardly, undignified and inhumane".
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Speaking after Sunday's Regina Coeli, Pope Francis said: "I am particularly close to the dear people of Indonesia, especially to the Christian communities of the city of Surabaya, which have been severely hit by the serious attack on places of worship".
Jemaah Islamiyah, the network responsible for the Bali attacks, was obliterated by a sustained crackdown on militants by Indonesia's counter terrorism police with USA and Australian support.
Indonesian police have foiled numerous terror plots, but the coordinated nature of Sunday's church bombings and the subsequent blasts point to more sophisticated planning than in the past, analysts said. More bombs were found at the family home.
ISIS first mounted attacks in Indonesia in 2016, claiming the lives of four civilians in explosions and shootings. The father of one of the suicide bombing families was the head of his local branch. Investigators believe the parents belong to Jamaah Ansharut Daulah, a terrorist group that lends its support to ISIS in Indonesia, the police general said.
He said the imprisonment of JAD's leader, Aman Abdurrahman, could be another motive, and cited clashes with Islamist prisoners at a jail near Jakarta last week in which five counter-terrorism officers were killed.
Karnavian said the family had returned to Indonesia from Syria, where until recently the Islamic State group controlled significant territory. Nearly 10% of the population is Christian.