JAKARTA - A family of suicide bombers was responsible for the latest in a series of suicide bombings in Surabaya, the capital of East Java province, said Indonesia's National Police Chief Tito Karnavian on Monday (May 14).

The latest attack was carried out by a family of five that included an eight-year-old child, Tito told reporters. The child survived and is now recovering.

On the motives for Monday's bombing, Tito said the attackers received instruction from the headquarters of Islamic State in Iraq and Syria (ISIS).

They were told to carry out the attacks in retaliation for the arrest of radical cleric Aman Abdurrahman. The cleric is on trial for masterminding a 2016 terror attack in central Jakarta that killed four.

He is being detained on the Nusa Kambangan prison island in central Java and is scheduled to appear in court on Friday (May 18).

The militants were also seeking revenge for the arrest of Zainal Ansori, the head of East Java chapter of ISIS-affiliated terror network Jemaah Ansharut Daulah (JAD) last year.

"They received instruction from the ISIS central command. They are being squashed there and issued instructions to their cells around the world to make a move," General Tito said. The father was from the same terror cell as the family of six who attacked three churches on Sunday, the police chief told reporters.

The family, riding on two motorcycles, blew themselves up at a checkpoint outside the Surabaya police headquarters at 8.50am on Monday.

At least 10 people were injured at the scene, a day after a family of suicide bombers attacked three churches, leaving at least 12 people dead and more than 40 injured.

Gen Tito told reporters that Monday's attack involved a highly volatile and destructive explosive nicknamed the "Mother of Satan". Such bombs can be put together using easily procured materials which are then mixed with other substances.

Coordinating Political, Legal and Security Affairs Minister Wiranto said the police backed by the military would step up security across the country.

“The president has commanded that police, helped by TNI (the armed forces), to exert all power to secure the nation,” retired army General Wiranto told reporters.

East Java provincial police spokesman Frans Barung Mangera told reporters four police officers and six civilians were injured in Monday morning's blast.

A number of police officers and civilians were caught in the blast, he said.

Closed-circuit television footage of the attack showed a two-wheeler carrying a man and a woman being stopped by officers at the gates of Surabaya police headquarters shortly before the bomber detonated his explosives.

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A photograph taken by witnesses at the scene showed a policeman lying injured on the ground. Photographs and video footage of the attack site showed smouldering body parts and debris scattered by the police headquarters' gate.

A girl who survived the blast was swiftly carried away from the site, another eyewitness video showed.

In a press conference shortly after the attack, Indonesian President Joko Widodo said he would issue a 'perppu' (an emergency law in lieu of law) for anti-terror measures.

"If Parliament by June do not complete deliberation of the draft anti-terror law that my administration proposed in February 2016, I will issue a perppu," Mr Joko said.

"This is a cowardly act. They have no dignity. They are barbaric. I need to reaffirm that we will fight terrorism, extinguish its roots," he added.

The government has proposed a stronger anti-terror law that allows police to take preemptive measures in fighting terrorism. The current law requires police to have ample evidence or wait till an operation or attack is launched before police can make arrests.

Gen Wiranto told reporters after meeting lawmakers on Monday: "Law enforcement officials are now in a handcuffed condition when dealing with terrorists. This must change."

Gen Wiranto said that with a stronger law, police can act fast as they not only have guns, but also ample authority and confidence to act.

"When there is early indication, they can make their move already."

Gen Wiranto dismissed worries that there was scope for the authorities to misuse the stronger anti-terror law for political purposes.

Meanwhile, the police killed one suspected terrorist and arrested three others in two locations in Sidoarjo regency earlier on Monday, MetroTV reported. The police have not confirmed the report.

One of the two raids in Sidoarjo was at the Puri Maharani residential complex, MetroTV reported.

Local residents heard gunshots before police raided a house occupied by a terrorist identified as Budi. The police seized six pipe bombs from the house.

MetroTV footage showed yellow police line tape cordoning off Budi's house.

Monday's bombing marked the third time in two days when whole families have turned suicide bombers, killing themselves and others.

The family which bombed three churches on Sunday had six members who killed themselves, while a separate blast in Sidoarjo later that evening left three members of a family of six dead. The blast on Monday killed four suicide bombers from the same family, with only a young child surviving.

There is also understood to be a fourth family that is on the run after being identified by the police as being the idealogues behind the church bombings.

Police across the country are on the highest level of security alert following the attacks, including in Jakarta, the Riau Islands and East Java.

Bali has also been on high alert since last Tuesday evening, following a deadly riot involving terrorist inmates at a detention centre located at the police’s Mobile Brigade (Brimob) headquarters in Depok, West Java.

Meanwhile, national police spokesman Inspector General Setyo Wasisto said at a press conference the police was concerned by the circulation of photos and videos that contain violence.

The police were also concerned about the spread of hoaxes about other raids and bombing attacks that never occurred.

"We appeal to everyone to not post photos, videos that show violence‎. If you have any on your gadget, please delete them. Sharing any of those amounts to spreading terror," said Inspector General Setyo.