Police said they killed four suspected members of JAD in Cianjur, West Java Province, and arrested two others, the BBC reported. Police said it was as though they wanted to be easily identifiable.
The attacks killed 25 people, 13 of whom were the suicide bombers, and injured dozens more.
Such groups, which are loyal to the Islamic State in Iraq and Syria, as well as returnees from ISIS territories in the Middle East, pose a growing new threat in Indonesia, said Mr Evan Laksmana, a senior researcher at the Jakarta-based Centre for Strategic and International Studies.
But observers say that there is certainly a whiff of ISIS in the strikes on the churches and the local police station by two families, as well as the plot that was botched up by a third family in nearby Sidoarjo after their bombs exploded prematurely.
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.
All told, 25 people have died since Sunday including a total of 13 militants and their children.
It claimed responsibility for 11 attacks between 2000 and 2010, including the deadly 2002 Bali bombings that left more than 200 people dead and hundreds injured, many of them tourists.More news: 'Gotham' renewed for fifth and final season
Officials have identified Oepriarto as the head of Jemaah Ansharut Daulah (JAD), an Indonesian IS-inspired network.
Terrorist in Indonesia made police their main target after a number of their leaders and fellow terrorist fighters were arrested or killed by special anti terrorist police squad.
Coordinated suicide bombings at three churches were carried out Sunday by a family of six that included girls aged 8 and 12. "Now if you go to the airport, there's a tight security check, and even if you go to some housing areas and malls they are also conducting security checks", Michelle said.
Earlier Tuesday, police searched the home of the family that bombed Surabaya's police headquarters.
Oepriarto blew himself up at Surabaya Center Pentecostal Church, while his two sons killed themselves at Santa Maria Roman Catholic church. An eight-year-old girl is the only surviving family member.
Indonesia's latest wave of terrorist bombings, the worst since 2009, have killed at least 14 people.
"According to police, on Sunday morning, "Two young boys aged 16 and 18 rode a motorcycle into a church courtyard and detonated their explosives".