The Abdallah Azzam Brigades, an al-Qaida offshoot, said it would maintain Majid's "project," the (Beirut) Daily Star reported Monday.
"Majid passed away after he laid the foundations for an ambitious project and after years of raising up men capable of managing his project after his passing," the group said in a statement.
Majid died Jan. 4 in a Lebanese military hospital after being captured by security forces in December.
The group added Majid "personally oversaw" the twin suicide bombings of the Iranian embassy in Beirut.
He was wanted by the United States and Saudi Arabia and other Arab countries on terrorism charges.