A family of six launched suicide attacks on Christians attending Sunday services at three churches in Indonesia's second-largest city of Surabaya, killing at least 13 people and wounding 40. 

Indonesia, the world's largest Muslim-majority country, has seen a recent resurgence in homegrown militancy and police said the family who carried out Sunday's attacks were among 500 Islamic State sympathizers who had returned from Syria. 

'The husband drove the car, an Avanza, that contained explosives and rammed it into the gate in front of that church,' East Java police spokesman Frans Barung Mangera told reporters at the regional police headquarters in Surabaya.

The wife and two daughters were involved in an attack on a second church and at the third church 'two other children rode the motorbike and had the bomb across their laps', Mangera said.

The two daughters were aged 12 and 9 while the other two, thought to be the man's sons, were 18 and 16, police said 

Mangera said explosions took place in three churches and at least 13 had died and 40 had been taken to hospital. He called on people to remain calm.

'All places where the public can gather, security has been tightened in those places,' he told a news conference. 

Television footage showed one church where the yard in front appeared engulfed in fire, with thick, black smoke billowing up. A large blast was heard hours after the attacks, which Mangera said was a bomb disposal squad 'securing' a remaining device.

ISIS claimed responsibility for the attack, the Islamist militant group's Amaq news agency said, without providing any evidence.

'Three martyrdom attacks inflicts at least 11 deaths and 41 injuries of the churches' guards and Christians in the city of Surabaya in East Java province in Indonesia,' the agency said in a statement that gave no further details. 

Police blamed the bombings on the Islamic State-inspired group Jemaah Ansharut Daulah (JAD). 

JAD is an umbrella organization on a US State Department 'terrorist' list that is estimated to have drawn hundreds of Islamic State sympathizers in Indonesia.

The attacks come days after militant Islamist prisoners killed five members of an elite counter-terrorism force during a 36-hour standoff at a high security jail on the outskirts of the capital, Jakarta.

The church attacks were likely linked to the prison hostage standoff, Purwanto said.

'The main target is still security authorities, but we can say that there are alternative (targets) if the main targets are blocked,' he said.

At St Mary's catholic church, one of the places of worship attacked, the bombing happened after an earlier mass was over and when the church was getting ready to hold another service.

Inspector general Machfud Arifin told CNN Indonesia that the suicide attacks were carried out using a motorbike at St Mary's church and a car at another.

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.

Television images showed toppled and burnt motorcycles and debris scattered around the entrance of one church and police cordoning off areas as crowds gathered.

Nearly 90 per cent of Indonesians are Muslim, but the country is also home to sizeable communities of Hindus, Christians, Buddhists, and people who adhere to traditional beliefs.

Indonesia has had some major successes tackling militancy inspired by al Qaeda's attacks on the United States in 2001. But there has been a resurgence of Islamist activity in recent years, some of it linked to the rise of Islamic State.

The most serious incident was in January 2016 when four suicide bombers and gunmen attacked a shopping area in central Jakarta.

Churches have also been targeted previously, including near-simultaneous attacks on churches there at Christmas in 2000 that killed about 20 people.

Police ordered the temporary closure of all churches in Surabaya on Sunday, and a large food festival in the city was cancelled.