Thirteen people were killed and 46 injured Sunday in suicide bombing attacks on three churches in Indonesia's second-largest city Surabaya, with authorities saying they were carried out by a family of six including four children aged between 8 and 17.

In a statement carried by its Amaq news agency, the Islamic State terrorist group claimed responsibility for the bombing attacks, but without providing details or evidence to back up the claim.

President Joko "Jokowi" Widodo condemned the terrorist acts as "extremely barbaric and beyond the limits of humanity," citing the targeting of innocent worshippers during Sunday morning mass services and the use of children.

National Police Chief Gen. Tito Karnavian said that the mother and her two daughters, aged 8 and 12, were the bombers at one church, her two sons, aged 15 and 17, attacked a second church, and the children's father blew himself up at a third.

All six members of the family, who had just returned from Syria, died, Tito told a press conference.

"The father dropped his wife and two daughters at the Indonesian Christian Church, where the mother and daughters blew themselves up with belt bombs, damaging their abdomens," he said.

Meanwhile, driving on a motorcycle, the family's sons blew themselves up at the Santa Maria Tak Bercela (Unsinful St. Mary) church, according to Tito.

[All photos Getty/Kyodo]

"One of the sons carried the bomb on his lap, while the other drove the motorcycle," he said. "We don't know the type of the bomb, but it caused a big explosion."

The father drove his bomb-laden Toyota van to the Central Pentecost Church and detonated it. "This was the biggest among the three bombing attacks because it used a car bomb," the top police officer said.

East Java police spokesman Frans Barung Mangera told reporters that the attacks occurred between 7:30 a.m. and 8 a.m. when the churches were holding their morning mass services.

The bombings at 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.

During an interview with the Jakarta-based private television network Metro TV, State Intelligence Agency spokesman Wawan Hari Purwanto said intelligence reports had detected a possible terrorist attack on May 11, "but apparently they changed it to (the) 13th."

"National and local police headquarters became their main target, while religious houses became their alternative or emergency targets," Wawan said.

"They operated like playing a cat-and-mouse game with police, targeting police headquarters but changing it to religious houses when they found out that the police headquarters were tightly guarded," he added.

The intelligence agency suspects the perpetrators were members of the Islamic State-linked Jamaah Ansharut Daulah.

Following the attacks, the East Java Police Headquarters instructed all churches in Surabaya not to hold mass services.

"I was supposed to get involved in the church choir at Alfons Gonzaga Catholic Church today, but the church suddenly stopped the mass service and asked the churchgoers to go home," churchgoer Ida Susanti told Kyodo News.

In another development Sunday, four terrorist suspects were shot dead by counterterrorism unit Detachment 88 in the town of Cianjur in West Java Province at 2 a.m. as they were allegedly on their way to attack the headquarters of the Mobile Brigade, an elite police unit, in Depok, in the suburbs of Jakarta.

At the Mobile Brigade's detention center in Depok, a riot by Islamic militant inmates earlier in the week led to the deaths of five police officers and an inmate.

After the rioting began at the detention center Tuesday, radical Muslim groups called via social media for their followers to go to the brigade's headquarters to help the inmates fight the police.

"The four suspected terrorists were shot because they fought against security apparatus who were going to arrest them," Cianjur Police Chief Soliyah, who like many Indonesians goes by a single name, told reporters, adding that the suspects had been followed by counterterrorism policemen from the town of Sukabumi, about 27 kilometers away.

"The security apparatus also seized two revolvers, three bags of explosives...and other evidence," she added.

On Saturday, two women were arrested on suspicion of planning to attack members of the Mobile Brigade at its headquarters.

"We still continue interrogating them to verify if they are members of a terrorist network," National Police spokesman Muhammad Iqbal said.

Early questioning found that the women, 18 and 21, planned to stab policemen at the headquarters using scissors.

The spokesman said the women, one wearing a hijab and the other wearing a niqab, were arrested after police observed them acting suspiciously -- going back and forth in front of the headquarters.

Police seized from them cellular phones and bus tickets they bought to travel from their hometowns in Ciamis in West Java Province and Temanggung in Central Java Province to Jakarta. It was not immediately clear when the women arrived in Jakarta.

On Thursday, four Islamist militants were arrested in the town of Bekasi in West Java Province after police received intelligence reports that they were on their way to the detention center to help the rioting detainees fight the police.

While being brought to Jakarta for questioning, two of the four men attacked policemen who were escorting them and tried to grab their weapons. The policemen shot them, killing one and injuring the other. Weapons and ammunition were seized from them.

Early investigations showed that the four men were members of the Jamaah Ansharut Daulah.

Also on Thursday, a Mobile Brigade intelligence officer was stabbed to death by a 22-year-old university student when the former was about to question the latter for acting suspiciously inside the brigade's headquarters.

The student died after being shot by another policeman.

The series of terrorist attacks in the past week, according to terrorism expert Harits Abu Ulya, showed that the call on social media following the riot at the Mobile Brigade Headquarters has "sparked terrorist cells across the country to launch attacks."