At least 41 people were injured in the bombings, which Indonesia's president condemned as "barbaric".
The UN chief was appalled at reports that children were used to participate in the attacks, said Guterres' spokesman Stephane Dujarric in a statement.
The bombings at the Christian churches occurred in the capital of Indonesia's East Java Province shortly after a series of attacks on police took place elsewhere in Indonesia following Islamist rioting at a detention center at the headquarters of elite police unit the Mobile Brigade in Depok, near Jakarta.
According to Karnavian's chronology of events, which doesn't line up with the sequence Mangera previously provided to the state-run Antara news agency, the father, identified as Dita Sopriyanto, drove a van to the Indonesian Christian Church and dropped off wife Puji Kuswat and their 9- and 12-year-old daughters.
Karnavian said Futrianto drove a bomb-laden auto into the city's Pentecostal church.
The attackers included two daughters aged 9 and 12 years old, said Head Gen. Tito Karnavian, the country's highest-ranking police official.
It is not yet known if this bombing was connected to the other attacks.
"Right now there are only three locations".
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"Suddenly, she hugged a civilian, then [the bomb] exploded", said the eyewitness, who identified himself as Antonius.
Indonesia's Foreign Minister Retno Marsudi tweeted condolences to the bombing victims with the hashtags #UnitedAgainstTerrorism and #WeAreNotAfraid.
"These attacks on peaceful worshipers are an affront to the tolerance and diversity embraced by Indonesians".
Noting that the heinous attacks resulted in the loss of innocent lives and caused injuries to many, Singapore expressed its deepest condolences to the bereaved families and wished the injured a quick recovery. Police said the members of the family that carried out Sunday's attacks were among 500 Islamic State sympathisers who had returned from Syria.
Indonesia is the world's most populous Muslim country with more than 82% of its roughly 260,500,000 people following Islam. Nearly 10% of the population is Christian.
They blamed the bombings on the Islamic State-inspired group Jemaah Ansharut Daulah.
"We suspect it is a suicide bomb attempt".
But the country's deadliest jihadist attacks predate IS.