Suicide bombers from the same family killed at least 13 people and wounded 41 in attacks on Christians attending Sunday morning services at three churches in Indonesia.

All six family members were killed in the attacks in Surabaya and at least 41 people were injured, in acts that Indonesia's president condemned as 'barbaric'.

The bombings were the worst to target churches in Indonesia since a series of attacks on Christmas Eve in 2000 killed 15 people and wounded nearly 100.

Religious minorities in Indonesia, especially Christians, have been repeatedly targeted by militants.

National police chief Tito Karnavian said that the father exploded a car bomb, two sons aged 18 and 16 used a motorcycle for their attack, and the mother was with daughters aged 12 and nine for her attack.

Mr Karnavian said the family had returned to Indonesia from Syria, where until recently the Islamic State group controlled significant territory.

Smoke billows from burning debris at a church in Surabaya, East Java, Indonesia May 13, 2018

An Indonesian anti-terror policeman stands guard at the blast site following a suicide bomb outside a church in Surabay

A member of the police bomb squad unit examines the site of an explosion outside the Immaculate Santa Maria Catholic Church, in Surabaya, East Java

Firefighters are seen at the site of a blast at the Pentecost Church Central Surabaya after the savage attacks

Police assist a woman looking for family members near the site of a blast at the Pentecost Church Central Surabaya after the gruesome attacks

Indonesian anti-terror policeman stands guard at the blast site following a suicide bomb outside a church in Surabaya today

Police stand guard as Christian devotees attend a Sunday mass at the Saint Petrus church in Bandung after the blasts today

The extremist group claimed responsibility for Sunday's attacks in a statement carried by its Aamaq news agency.

The first attack struck the Santa Maria Roman Catholic Church in Surabaya, police spokesman Frans Barung Mangera told reporters.

That blast was followed by a second explosion minutes later at the Christian Church of Diponegoro and a third at the city's Pantekosta Church.

A witness described the woman's attack at the Diponegoro church, saying she was carrying two bags when she arrived.

'At first officers blocked them in front of the churchyard, but the woman ignored them and forced her way inside. Suddenly she hugged a civilian then (the bomb) exploded,' said the witness, a security guard who identified himself as Antonius.

An armed member of the Indonesian Mobile Brigade Corps stand guard during Asian Games preparation carnival on a main street in Jakarta after the savage attack today

Members of police bomb squad inspect wreckage of motorcycles at the site where an explosion went off outside a church

Officers walk past debris at Santa Maria church where an explosion went off in Surabaya, East Java

Debris are seen at a church where an explosion went off in Surabaya, East Java, Indonesia

A person injured from a blast at the Indonesian Christian Church is evacuated to a waiting ambulance in Surabaya

Firefighters try to extinguish a blaze following a blast at the Pentecost Church Central Surabaya

People carry a body bag containing a victim of a bomb blast at The Immaculate Santa Maria Church, at Surabaya Surgical Hospital in Surabaya

K9 police examine a site following attacks outside the Surabaya Centre Pentecostal Church after the grim blasts

Mr Mangera said three unexploded homemade bombs - two at the Pantekosta church and one at the Diponegoro church - were detonated by a bomb squad.

Shattered glass and chunks of concrete littered the entrance of the Santa Maria Church, which was sealed off by armed police.

Rescue personnel treated victims at a nearby field while officers inspected wrecked motorcycles in the car park that had been burned in the explosion.

A street merchant outside the church said she was blown several metres by the blast.

'I saw two men riding a motorbike force their way into the churchyard. One was wearing black pants and one with a backpack,' said the merchant, Samsia, who uses a single name. 'Soon after that the explosion happened.'

President Joko 'Jokowi' Widodo visited the scenes of the attacks and described them as 'cowardly actions' that were 'very barbaric and beyond the limit of humanity'.

In Jakarta, Indonesia's capital, the Indonesian Church Association condemned the attacks.

'We are angry,' said Gormar Gultom, an official with the association, who urged people to let the police investigation take its course.

Indonesia's two largest Muslim organisations, Nahdlatul Ulama and Muhammadiyah, also condemned the attacks.

Separately, national police spokesman Setyo Wasisto said police fatally shot four suspected militants and arrested two others early on Sunday in West Java towns. It was not clear whether the shootings were connected to the church attacks.

'They have trained in order to attack police,' Mr Wasisto said, identifying the militants as members of Jemaah Anshorut Daulah, an Islamic State group-affiliated network of about two dozen extremist groups that has been implicated in a number of attacks in Indonesia over the past year.

Jakarta police placed the capital and surrounding areas on high alert, while the transportation ministry warned airports to be on guard.

The church attacks came days after police ended a hostage-taking ordeal by imprisoned Islamic militants at a detention centre near Jakarta in which six officers and three inmates died. IS claimed responsibility.

Indonesia has carried out a sustained crackdown on militants since bombings by al Qaida-affiliated radicals in Bali in 2002 killed 202 people. In recent years, the country has faced a new threat as the rise of IS in the Middle East invigorated local militant networks.

Christians, many of whom are from the ethnic Chinese minority, make up about 9% of Indonesia's 260 million people.

Police officers stand guard near the site where an explosion went off at Santa Maria church in Surabaya

A damaged motorbike is seen at the scene outside a church following a suicide bomb in Surabaya

Indonesian bomb squade examine the site following a suicide bomb outside a church in Surabaya

Indonesian bomb squad police officers inspect a blast site in front of a church in Surabaya, East Java, Indonesia

Two armed members of the Indonesian Mobile Brigade Corps stand guard during Asian Games preparation carnival on a main street in Jakarta

The church attacks came days after police ended a hostage-taking ordeal by imprisoned Islamic militants at a detention center near Jakarta in which six officers and three inmates died. IS claimed responsibility.

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.

Pope Francis prayed for victims of the suicide bombing.

Francis on Sunday expressed his spiritual closeness to the Christian community in Indonesia, especially in Surabaya.

Francis asked faithful in St. Peter's Square to join him in prayers to the 'God of peace so that he will make these violent actions stop, and that in the hearts of all there will be room not for sentiments of hatred and violence but of reconciliation and brotherhood.'

The pope has often draw attention to minority Christian communities that have been targets of persecution or other violence.