Aman Abdurrahman allegedly set up Jemaah Ansharut Daulah (JAD) in 2014 to bring together the Indonesian supporters of the Islamic State group.
Authorities have blamed JAD for a string of suicide bombings in the city of Surabaya this week, which killed about 30 people, including 13 of the suspected bombers.
Aman was already on trial when the bombings happened.
He is also said to be responsible for the 2016 Jakarta bombings, when eight people were killed in attacks on a Starbucks cafe and a police post nearby.
The defendant was previously sentenced to nine years in prison for training militants in Aceh and seven years behind bars for a bombing in Cimanggis, in East Java in 2004.
Prosecutor Anita Dewayani asked for the death penalty, the first time it has been requested for a terrorist case since the bombing of the Australian embassy in 2004.
“Aman Abdurrahman is not in the structure of JAD as the leader, but he was being positioned as a reference point above the Amir [ruler] of JAD” she told the court.
“We demand the south Jakarta District Court … determine that Aman Abdurrahman has been legally and convincingly proven to be guilty of terrorism … [and] to hand down the punishment of death to the defendant.”
Aman spent time in the same prison as Rois, the Australian Embassy bomber on death row.
He has also given regular sermons to inmates and visitors during his time behind bars.
He is being held at the high-security Jakarta prison, where last week more than 150 inmates rioted, killing five elite Indonesian police.
During the standoff, inmates demanded to speak to Aman, and negotiators allowed the meeting.
The prison riot delayed today’s court hearing.
Aman’s lawyers will read his plea and defence next week.