Suicide bombers targeted Sunday Mass congregations in three churches in Indonesia's second-largest city, killing at least 13 people and wounding dozens in one of the worst attacks on the Christian minority, police said.

The first attack struck the Santa Maria Roman Catholic Church in Surabaya, killing four people, including one or more bombers, police spokesman Frans Barung Mangera told reporters at the scene. He said two police officers were among a total of 41 wounded.

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

Daesh terror group claimed responsibility for the attack later on Sunday through its Amaq news agency said, without providing any evidence.

"Three martyrdom attacks inflict 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.

According to the Indonesian police, the attackers all belonged to the same family of six.

The family — a mother and father, two daughters aged 9 and 12, and two sons aged 16 and 18 — had returned to Indonesia from Syria.

President Joko "Jokowi" Widodo arrived in Surabaya, the East Java provincial capital, in the aftermath of the attacks, Mangera said. The bombings were the worst since a series of attacks on churches on Christmas Eve in 2000 killed 15 people and wounded nearly 100. Religious minorities, especially Christians, have been repeatedly targeted by militants.

A senior police official said the bombings were carried out by at least five suicide bombers, including a veiled woman who had two children with her. The official spoke on condition of anonymity because he wasn't authorized to speak to the media.

A witness described the woman with children, saying she was carrying two bags at the Diponegoro church.

"At first officers blocked them in front of the churchyard but the woman ignored and forced her way inside. Suddenly she hugged a civilian then (the bomb) exploded," said a civilian guard named Antonius.

Shattered glass and chunks of concrete littered the entrance of the Santa Maria Church, which was sealed off by heavily armed police. Rescue personnel treated victims on a nearby field while officers inspected wrecked motorcycles in the parking lot that were burned in the explosion.

A street merchant outside the church said she was blown away several meters (yards) by the powerful blast.

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

In Jakarta, the Indonesian Church Association strongly condemned the attacks and called on people to wait on authorities to investigate.

"We are angry with these attacks, but we leave it to the authorities to resolve them," said Gormar Gultom, an official with the association.

National police spokesman Setyo Wasisto announced that police fatally shot four suspected militants and arrested two others early Sunday in West Java towns. It wasn't clear if the shootings were connected with the church attacks.

"They have trained in order to attack police," Wasisto said, identifying the militants as members of Jemaah Anshorut Daulah, or JAD. The network of about two dozen extremist groups has been implicated in a number of attacks in Indonesia over the past year. It pledges allegiance to Daesh leader Abu Bakr al-Baghdadi.

The latest attacks in predominantly Muslim Indonesia came days after police ended a riot and hostage-taking at a detention center near Jakarta that left six officers and three inmates dead. Daesh has claimed responsibility.

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

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