"Lebanon is in a dangerous situation," Abul Gheit said in an interview with local radio.
"Sunni Muslims have rights in Lebanon which they must protect," he added in response to a question.
Fears of Sunni-Shiite sectarian violence are rising as a political crisis deepens over a UN-backed tribunal probing the 2005 assassination of ex-premier Rafiq Hariri, himself a Sunni Muslim.
Syrian- and Iranian-backed Hezbollah earlier this month forced the collapse of the unity government of Saad Hariri, son of Rafiq, in a dispute over the Netherlands-based Special Tribunal for Lebanon (STL).
The Shiite group has said it expects the STL, which it claims is under US-Israeli control, to implicate Hezbollah members in the Hariri murder, warning any such accusation would have grave repercussions.
Abul Gheit on Sunday threw his weight behind the court, saying it was unstoppable.
"The tribunal cannot be stopped but the political developments in Lebanon may succeed in slowing it down," he said.
Lebanese President Michel Sleiman is scheduled to begin two days of talks on Monday with the country's parliamentary groups to appoint a new prime minister.
By longstanding tradition, Lebanon's premier must be a Sunni Muslim, its speaker a Shiite Muslim and its president a Maronite Christian.
Mainly Sunni Egypt has tense ties with the Shiite Hezbollah and its backer Iran.