Abssi and Fatah al-Islam first came to public attention in November when Lebanese authorities arrested two of the group's members.
"The Palestinian refugees are not being treated properly by Lebanon"
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Abssi, who was born in the West Bank town of Jericho but later fled with his family to Jordan, was freed from a Syrian jail last year and slipped into Lebanon where he made his base in the impoverished Nahr al-Bared camp.
Later on Tuesday heavy fighting erupted between the Lebanese army and the group’s fighters at the camp.
A military source described the fighting as heavier than usual on the outskirts of the camp, home to 40,000 before the fighting forced thousands to flee, mostly to a nearby refugee camp.
A senior military official said that the army was reinforcing its positions and "tightening the noose" on the fighters' inside the camp.
For the past three weeks, the army has been struggling to crush Fatah al-Islam despite its superior firepower.
On Monday, three soldiers and two Red Cross workers were killed and a mediator attempting to find a peaceful solution to the crisis was wounded in separate incidents around the besieged camp.
Since late Monday, sporadic gunfire was heard around the camp where about 3,000 civilians are still marooned by the fighting in increasingly desperate conditions.
Monday's deaths brought to 128 the number killed in the deadliest internal feuding since Lebanon's 1975-1990 civil war.
The death toll includes 61 soldiers and 50 members of Fatah al-Islam.