Counter-terrorism chief Ansyaad Mbai said the men were part of a violent Islamist group and were shot as the anti-terror police unit Detachment 88 conducted a raid on the street in an East Java town. (Agencies)
"Detachment 88 had sought the men over a recent attempted suicide bombing and a case of hacking to fund militant activities," Mbai said.
The police squad ambushed the men as they waited for public transport in Tulungagung district, national police spokesman Boy Rafli Amar said.
One of those killed, identified as Dayah, "took out a weapon and began firing at the squad, which led to a gunfight", Amar told reporters.
"Two suspects died and the other two surrendered and were arrested," Amar said.
The other suspect shot dead was identified only as Rijal. Police seized a revolver and a bag containing a homemade bomb.
Mbai connected the men to an attempted suicide bombing in June on a police compound in Poso -- a district on Sulawesi island known for militant activity.
The bomber blew himself up, only injuring a construction worker. It was the first suicide attack in Indonesia since September 2011, when a bomber injured dozens in an attack on a Central Java church.
Police have said the suicide bomber was suspected of being part of the Eastern Indonesia Mujahideen Islamist terror group -- headed by Santoso, Indonesia's most wanted militant.
The group hides out in the jungles around Poso and is suspected of carrying out a series of attacks, including police killings.
Santoso appeared in a video posted online earlier this month urging "jihad" and calling Detachment 88 a "real enemy".
Indonesia has been waging a campaign against Islamist terror groups for more than a decade and has largely dismantled some of the deadliest groups, with only low-impact attacks carried out in recent years.
Counter-terrorism chief Ansyaad Mbai said the men were part of a violent Islamist group and were shot as the anti-terror police unit Detachment 88 conducted a raid on the street in an East Java town.