Indonesian police have arrested 37 suspects in connection with the suicide bombings in Surabaya last month, the country's top cop Tito Karnavian has said.

Four other suspects were shot and killed by police in the dragnet to bring to justice those responsible for the attacks on three churches on May 13, as well as one on the local police station the next day in Indonesia's second-largest city.

"We moved fast after the suicide bombings... and identified the perpetrators," said General Tito, adding that the swift response by the police should continue to give the public a sense of security.

He was speaking to reporters on Thursday night after breaking fast with Indonesian armed forces chief Hadi Tjahjanto during their visit to the Surabaya police headquarters.

The police chief did not reveal the identities of the suspects, but confirmed that they were linked to the coordinated suicide bombings in Surabaya mounted by two separate families, as well as a botched plot by a third family in nearby Sidoarjo in which the bombs exploded prematurely.

A total of 27 people were killed in the attacks, and the dead included the 13 perpetrators who were said to be members of sleeper cells of the Jemaah Ansharut Daulah (JAD), a local terrorist group loyal to the Islamic State in Iraq and Syria (ISIS).

Traces of military-grade explosives found at the attack sites, and the fact that women and children were used as cover for the suicide bombings, suggest a rising level of tactical capability among Indonesian terrorists.

The incidents in Surabaya, which occurred days after a hostage situation at a police detention centre housing JAD detainees, have since led to the passing of amendments to Indonesia's anti-terror laws, designed to prevent terrorist attacks. The changes passed by Parliament on May 25 include allowing the police to make pre-emptive arrests and hold terror suspects longer for investigations, having the military support the police in counter-terrorism at home and making it an offence to join foreign militant groups such as ISIS.

Gen Tito said there were lessons learnt from the recent spate of terror-related incidents. "First, that such a beautiful city like Surabaya can become a target of terrorism," he said. "Second, terrorism these days involves families, including mothers and their children."

Separately, the National Counter-terrorism Agency on Thursday signed a memorandum of understanding with the Ministry of Law and Human Rights to share information on foreign terrorist fighters (FTFs) and terrorist inmates currently held in Indonesia's prisons. FTFs typically refer to Indonesians who have joined groups such as ISIS overseas.

The latest figures indicate that at least 1,489 Indonesian citizens have joined ISIS, or have left home to try to link up with the extremist group in Syria, sometimes taking their families with them. More than 600 of these have returned home on their own or were deported.