The Saudi-born Majed , who claimed responsibility for a November attack on the Iranian embassy in Beirut that killed at least 23 people, died after his arrest by Lebanese authorities.
"His project will continue, God willing, in striking Iran, its party (Hezbollah) and the aggressor Jews (Israel), and in defending oppressed Sunnis everywhere," the group said in an online statement.
The statement also lashed out against Lebanon for "arbitrarily detaining" Islamists , and said Lebanese military intelligence was under the control of "Iran's party," a reference to Hezbollah.
It criticized "attacks against Sunnis orchestrated by Iran's party, which controls Lebanon's military intelligence and manipulates it at will."
It also said Iran "manipulates all Lebanese state institutions to protect both its interests and those of its Baathist ally in Syria," a reference to President Bashar al-Assad. 
Lebanese authorities said he died from poor health on January 4 , days after he was arrested, and his body was sent back to Saudi Arabia.