In his message, the grand Ayatollah described the late Ayatollah Asefi as an Alim Amil (a scholar who acts upon all the teachings of the religion).
A number of other scholars, religious personalities and political figures, including Iraqi Prime Minister Heidar al-Abadi also issued messages of condolences over the passing of the senior cleric.
Abadi said Ayatolah Asefi spent his life on the path of knowledge and struggling against oppression and tyranny.
Ayatollah Asefi passed away on Thursday morning shortly after his morning prayer. He had long been suffering from liver cancer.