Jakarta, May 14 (IANS): A family of six, who carried out three church bombings in Indonesia killing 13 persons, had returned from Syria, police said.

The Islamic State (IS) terror group has claimed responsibility for the attacks that took place on Sunday, the BBC reported.

A mother and two daughters blew themselves up at a church, while the father and two sons targeted two others in Indonesia's second city, Surabaya.

National police chief Tito Karnavian said they belonged to an IS-inspired network, Jemaah Ansharut Daulah (JAD).

The police said the family were among hundreds of Indonesians, who had returned from Syria, where IS has been fighting government forces, the BBC reported.

No details were given about the family's alleged involvement in that conflict.

The bombings are the deadliest in Indonesia in more than a decade, and also left more than 40 people injured.

Visiting the scene of one of the attacks, President Joko Widodo described them as "barbaric", adding that he had ordered police to "look into and break up networks of perpetrators".

The police identified the father as Dita Oepriarto, saying he was the head of a JAD cell in the area. He reportedly dropped off his wife, Puji Kuswati, and their two daughters -- aged nine and 12 -- at Diponegoro Indonesian Christian Church, where they blew themselves up.

He then drove off, launching his own bomb-laden car into the grounds of Surabaya Centre Pentecostal Church, the police said.

The sons -- aged 16 and 18 -- rode motorcycles into Santa Maria Catholic Church, and detonated explosives they were carrying. It was their attack that came first, at around 7.30 a.m. The other two attacks followed five minutes apart, the police said.

Later on Sunday, another bomb exploded at an apartment complex in Surabaya, killing three persons. East Java's police chief, Mahfud Arifin, said that those killed were the perpetrators, not victims.

It is not yet known if this bombing was connected to the other attacks.

Officials reportedly foiled attacks against other churches, too. Also on Sunday, police said they killed four suspected members of JAD in Cianjur, in West Java province, and arrested two others.