The court statement said Jundallah (Soldiers of God) was responsible for the killing of 154 security personnel and civilians since 2003.
"[Rigi] collaborated and ordered 15 armed abductions, confessed to three murders, ordered the murders of tens of citizens, police and military personnel through bombings and armed actions," the statement read.
Rigi was arrested in February by Iranian intelligence agents when an aircraft he was on en route from Dubai to Kyrgyzstan was forced to land in Tehran.
Al Jazeera's Alireza Ronaghi, reporting from Tehran, said the execution of Rigi was "a severe blow" to Jundallah.
"Iranian authorities [say] that an order has been issued, a kind of a pardon, to all the members of Jundallah who put down their weapons and come ask for forgiveness," he said.
"We hear that more than 200 members of Jundallah have already done that after Abdolmalek was arrested.
"[The members] were his true followers and did whatever he wanted them to do. Now that he's gone they may have a lot of doubt in continuing his path."
Just days after Rigi was arrested, the group said it had appointed Muhammad Dhahir Baluch as its new leader.
Baluch issued a statement saying the government would "face a movement that is stronger and much more solid than ever before".
But Mahjoob Zweiri, an expert in Iranian affairs at Qatar University, said the group no longer represented a major threat.
"Now, four months after his [Rigi's] capture there was nothing," he told Al Jazeera.
"No statement, no announcement, no activity. So there is a big question mark about the ability of this group to act."
Rigi's younger brother Abdulhamid was executed last month.
Iran has repeatedly said that Jundallah is backed by the United States.
The US has dismissed these claims as propaganda.