Anton died after police officers gunned him down to prevent him from triggering another bomb.
Christians are calling for prayer after several churches were attacked in Indonesia - with a single family suspected of carrying out the bombings.
"The Surabaya cell and the Sidoarjo cell are the same network because they met regularly on Sunday evening", said Arifin, referring to the three families behind the attacks.
A Surabaya police spokesman said police arrested 13 suspects over the two suicide bombings carried out by two families, after conducting raids in Surabaya and its neighbouring cities of Malang and Pasuruan.
He said the church bombers and the police headquarters attackers were friends, as were another family whose homemade bombs exploded in their apartment Sunday night.
Daesh claimed responsibility for all the attacks in statements carried by its Amaq news agency.
Democratic Party deputy secretary-general Rachland Nashidik said that while it was important to revise the Terrorism Law, the President should "pay attention to organizational reform and replace officials who have failed in carrying out their duties to protect the freedom and security of citizens".
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Twenty five people died in the two days of attacks including a total of 13 militants and their children.
Using women and children in militant attacks has always been a tactic deployed in other countries - Nigerian terror group Boko Haram often uses children as suicide bombers.
A security camera video of the attack on Surabaya's police headquarters showed at least one explosion after the four attackers rode two motorcycles up to a security checkpoint.
The attacks are thought to have been perpetrated in support of Jamaah Ansharut Daulah, an Indonesian jihadi group that supports ISIS.
The new spate of bombings comes just ahead of the holy Islamic month of Ramadan, and follows a melee at a detention center near Jakarta last week in which jailed Muslim extremists killed six officers. Its leaders were killed in police raids and hundreds of militants were arrested. The family's 12-year-old son reportedly took two younger sisters to the Bhayangkara Police Hospital.
Prime Minister Malcolm Turnbull said the use of children in the attacks was "sickeningly cruel".
Security remained tight around police buildings Tuesday in Surabaya, Indonesia's second-largest city. "While the father Dita Oepriarto, detonated a auto bomb outside a third church".