"There will be no compromise in taking action on the ground to stop terrorism", Widodo said. "We pray in silence".
The organization is known as the main supporter of the Islamic State militant group in Indonesia.
Like AR, FS, and GA, who suddenly became orphans, Ais, 8, the daughter of alleged suicide bomber Tri Murtiono, 50, also lost parents and two brothers during the suicide attack that involved two motorcycles at Surabaya police headquarters on Monday. Their mother Puji Kuswati attacked worshippers at another church with her daughters aged 9 and 12.
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.
The family's nextdoor neighbor, Abi Akbar, said Oepriarto and his sons, Yusuf and Firman, like almost all Muslim men in the neighborhood, usually attended dawn prayers at an unremarkable local mosque. The National Police Chief added that the bomb was named the "Mother of Satan" and was made by the mixing of explosive and reactive chemicals. "These attacks on peaceful worshippers are an affront to the tolerance and diversity embraced by Indonesians".
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The statement issued Sunday offered condolences to the families of victims and said the United Nations stands by Indonesia's efforts to fight extremism and prevent terrorism. Police killed the men after they had produced weapons during the raid and evidence confiscated included revolvers, bullets and an arrow with a bomb placed on the end of it, Wasisto said.
Police said they also shot dead four suspects, including the second-ranking member of the JAD cell in Surabaya, in raids on houses and offices Monday while nine others were arrested.
JAD is an umbrella organisation on a U.S. State Department "terrorist" list that is estimated to have drawn hundreds of Islamic State sympathisers in Indonesia.
Despite their apparent allegiance to IS, the church-bombing family were not returnees from Syria, police said Monday, correcting their earlier statements.
The Department of Foreign Affairs and Trade has issued a travel warning urging Australians to "exercise a high degree of caution in Indonesia, including in Bali, Surabaya and Jakarta, because of the high threat of terrorist attack".
Almost 90 percent of Indonesia's 260 million people are Muslim, but there are significant numbers of minority Christians, Hindus and Buddhists.