The cleric, a Saudi national, had voiced his objections during a meeting of an ISIS clerical body in the town of al-Bab in Aleppo province, said Rami Abdulrahman, who runs the Observatory.
The killing was been widely condemned by Muslim clerics. Even some al Qaeda-linked figures denounced it as un-Islamic.
A video released by ISIS militants on Tuesday showed the pilot, Muath al-Kassasbeh, being burnt alive in a cage.
The Saudi cleric had said those responsible for the killing should face trial, the Observatory said. Abdulrahman, whose organisation gathers information via a network of sources on the ground, said the group may now kill the cleric.
ISIS posted a religious edict on Twitter, which ruled that it is permissible in Islam to burn an infidel to death.
Muslim clerics have said it is forbidden to kill anyone that way.
