The children are believed to have had little or no contact with others outside their families and were shown jihadist videos by their parents, police said. Six civilians and four officers were wounded.
Three suicide blasts were committed by one family - a husband, wife and four children - against three churches in the town.
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.
On Monday morning a family of five also bombed the Surabaya police headquarters.
IS claimed responsibility for the church bombings in a statement carried by its Aamaq news agency.
Celtics finish off Philly, now it's time for LeBron
Atypically, the Celtics attacked the rim more than they launched 3-pointers, and the result was a relatively efficient first-half. After winning Game 4 in which Jayson Tatum exploded with 20 points, the Sixers saw something that they can continue for Game 5.
The flurry of bombings raised concerns that previously beaten-down militant networks in the world's most populous Muslim-majority nation have been reinvigorated by the return of some of the estimated 1,100 Indonesians who went to fight with the Islamic State group in Syria.
This is because the JI, and now the JAD, whose members have pledged their allegiance to ISIS, are indoctrinated to remain in a state of war, said Universitas Indonesia terrorism expert Ridlwan Habib.
And if the initial analysis by the police that the Jemaah Ansharut Daulah (JAD) is behind the recent attacks is accurate, then the local terrorist network has truly raised its game.
ISIS, from which the recent attackers reportedly took their cues, has always understood the power of using provocative violence, Barton said.
Elsewhere family and friends mourned the deaths of the 12 people killed in the church blasts.
Seann William Scott To Replace Clayne Crawford in 'Lethal Weapon' TV Series
FOX has chose to renew its action drama series Lethal Weapon for a third season, but it's not exactly that cut and dry. He said the first incident happened when he became angry with what he deemed unsafe working conditions on the set.
At least 26 people were killed and dozens more injured in the multiple suicide bombings, the deadliest terrorist strike in Indonesia in more than a decade.
Later in the day, police said another family attempted to carry out an attack the Surabaya suburb of Sidoarjo.
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.
Earlier, media reports said a woman with a younger child and a teenager had just entered one church and was being questioned by security when the bomb exploded.
The mother also participated in the attack alongside their daughters, aged 12 and 9.
Iran seeks 'clear future design' for imperilled nuclear deal
Zarif told Wang that maintaining the nuclear deal will serve Iran's interest. "We will try to uphold our side of the bargain". If the USA punishes European companies for doing business with Iran, foreign companies will likely walk away from Iran.
At Surabaya Centre Pentecostal Church, Futrianto then drove his vehicle onto the church grounds and detonated explosives.