The group planned to target government offices and foreigners in other Indonesian cities, a spokesman said.
So far, 12 arrests have been made in connection with Thursday's attack, which left two civilians dead and were claimed by Islamic State (IS).
Police have also shut down at least 11 websites and social media accounts.
One of the militants was named as Afif Sunakim, seen carrying a gun and rucksack during the attacks. He was given a seven-year jail term for attending a militant camp.
The guns used by the extremists came from the Philippines, police said.
Security forces battled militants for hours in the busy commercial district where the militants struck.
A Canadian and an Indonesian national died, and at least 20 people were injured.
The assault ended when two attackers died in a suicide bombing, police say, with the other three killed in gun battles.
Following recent IS threats, the country, which had been attacked by Islamist militants several times in the past, had been on high alert.
IS released a statement saying it had targeted citizens of countries which are part of the international coalition fighting the group, which controls parts of Syria and Iraq.