Indonesia’s police chief says a second suicide attack outside a police building in Surabaya, which wounded officers and civilians, was carried out by a family of five that included an eight-year-old child.

The family, riding on two motorbikes, blew themselves up at a checkpoint outside the police station on Monday, Police Chief Tito Karnavian said.

The young child survived and was now recovering, he said. Initial reports were that the child was a boy, but later reports said it was a girl.

On Sunday, another family of Islamist militants killed 13 people in suicide attacks on three churches in Surabaya.

Footage shows Monday’s blast at a security post at the entrance to the police complex. Several officers were injured.

Police suspect the new attacks are also by extremists linked to the Jemaah Ansurat Daulah group.

“Clearly it’s a suicide bombing,” East Java police spokesman Frans Barung Mangera said.

“We can’t be open [about] all details yet because we are still identifying victims at the scene and the crime scene is being handled.”

He said the full extent of casualties was unclear.

Indonesian President Joko Widodo said the series of suicide attacks in Surabaya was the “act of cowards” and pledged to push through a new anti-terrorism bill to combat networks of Islamist militants in the country.

“This is the act of cowards, undignified and barbaric,” Mr Widodo said on Metro TV.

He said he would issue a regulation in lieu of a law next month to force through a new anti-terrorism bill if Parliament failed to pass it.

The Pantekosta Centre Church after Sunday’s suicide bombing. Photo: Getty

Australian Prime Minister Malcolm Turnbull described the attacks as shocking and cowardly, and said he had written to Mr Widodo expressing Australia’s heartfelt sympathy.

“The brutality, the barbarity, the inhumanity, the blasphemy of these terrorists strains our ability to believe it but it’s there,” Mr Turnbull said.

“These people are the worst of the worst.”

There was another attack on a different police station in the city last night, about 12 hours after 14 people — including six suicide bombers — were killed in three separate attacks on Surabaya churches.

Members of one family were responsible for the church attacks, including a mother and two young girls wearing suicide belts.

The first attack, at the Santa Maria Roman Catholic Church, killed four people, including one or more bombers, a police spokesman said.

Minutes after the first, there was a second explosion at the Christian Church of Diponegoro that killed two people.

Another two people died in a third attack at the city’s Pantekosta Church, the police spokesman said.

-with AAP