In the first incident, the body of Shaikh Hazim al-Zaidi was found in front of al-Sajjad mosque in Sadr City, a mainly Shia area in eastern Baghdad on Monday, an AMS spokesman told Aljazeera.
There are reports he was abducted late on Sunday along with two others outside the mosque. Other reports indicate he was killed after leaving the mosque.
The shaikh was in charge of coordination among Muslim clerics within the AMS and other religious movements in Iraq.
In the second incident, later on Monday, Shaikh Muhammad Jadua was killed by armed men when he left al-Kauthar mosque in the Baya area, west of Baghdad.
The attackers struck just after the after noon prayers before fleeing.
AMS member Muthana Harith al-Dhari told Aljazeera: “We are still investigating the abduction and assassination of Shaikh Hazim and the assassination of Shaikh Muhammad Jadua to know whether they were two separate incidents or one incident as they took place on one day.
“The incidents indicate that the ASM is intentionally targeted,” he added.
Some Sunni and Shia groups have said they fear their members are being targeted by assassins, perhaps in an attempt to spark sectarian conflict in Iraq.
The AMS is a conservative group that has worked for the release of foreign hostages. It strongly opposes the US presence in Iraq – a position that has made it possible to act as an intermediary in hostage negotiations.
The 18 captured Iraqi National
The deaths follow the arrest of Shaikh Hazim al-Aaraji, a senior aide to Shia leader Muqtada al-Sadr in the early hours of Sunday.
He was detained by US forces and the Iraqi National Guard during a raid on his home.
A few hours after the arrest, a previously unknown group threatened to kill 18 captured Iraqi soldiers if the authorities did not release al-Aaraji within 48 hours.
But on Monday the group announced they had released the soldiers unharmed.