Attackers on motorbikes carried out a suicide bombing at a police headquarters in Surabaya, a day after a wave of deadly blasts in the Indonesian city.
Authorities said a young girl who was with the group, survived the attack, which wounded at least 10 people.
It comes after another family carried out bomb attacks on three churches on Sunday.
The Islamic State group has said it was behind those attacks.
Indonesia, the most populous Muslim-majority country, has seen a resurgence of Islamist militancy in recent months.
President Joko Widodo described the string of attacks as “cowardly, undignified and inhumane”.
“There will be no compromise in taking action on the ground to stop terrorism.”
Authorities on Monday said police, backed by military forces, would increase security across the country.
It was not yet clear whether the latest attacks were connected to deadly blasts on Sunday.
East Java police spokesman Frans Barung Mangera could not yet identify the four attackers, and revised an earlier report that two bombers carried out the bombing.
“A child who was with them, an eight-year-old girl… has been taken to the hospital,” he said.
What happened in Sunday’s attacks?
The latest attack follows four separate suicide bombings in Indonesia’s second largest city on Sunday.
Three took place at churches in Surabaya, carried out parents and their children.
Police have said the family were among hundreds of Indonesians who had returned from Syria, where IS has been fighting government forces. No details were given about the family’s alleged involvement in that conflict.
The father has been identified as Dita Oepriarto. Police say he was the head of local branch of Jemaah Ansharut Daulah (JAD), and Indonesian IS-inspired network.
In the first attack, the sons – aged 16 and 18 – rode motorcycles into Santa Maria Catholic Church at around 07:30 local time (00:30 GMT) and detonated explosives they were carrying.
The father then reportedly dropped off his wife, Puji Kuswati, and their two daughters at Diponegoro Indonesian Christian Church, where they blew themselves up. The girls – aged nine and 12 – had bombs strapped to them, as did their mother.
Oepriarto then drove off, launching his own bomb-laden car into the grounds of Surabaya Centre Pentecostal Church, police said.
Thirteen people were killed and more than 40 injured, making it the deadliest attack in Indonesia in more than a decade.
Later on Sunday, a bomb exploded at an apartment complex in Surabaya, killing three people, according to AFP news agency.
There was no immediate claim of responsibility for that attack.
What is the history of militancy in Indonesia?
The South East Asian country has long struggled with Islamist militancy. Its worst ever terror attack was in Bali in 2002, when 202 people – mostly foreigners – were killed in an attack on a tourist nightlife district.
That attack was carried out by the Jemaah Islamiah (JI) militant network.
But recent years have seen a number of attacks claimed by Islamic State (IS).
Four civilians and four attackers were killed in a series of explosions and shootings in central Jakarta in January 2016; the first attack claimed by the group.
In February this year, a number of people were injured in a sword attack at a church in Sleman, Yogyakarta. Police said that the attacker had previously tried to join IS in Syria.
