A senior security source told Reuters news agency: "The Lebanese army has seized the last positions of Fatah al-Islam in the camp.
"Most of the terrorists were killed today, the others have been captured. A few might have escaped but the army is hunting them down."
According to the army, Fatah al-Islam fighters attacked their positions while trying to escape the camp in northern Lebanon early on Sunday.
Lebanese troops killed at least 31 fighters.
Twenty-three more fighters from the Fatah al-Islam group, 12 of them wounded, were captured when they attempted to break out of Nahr al-Bared.
The army had estimated that 35 active fighters remained in the camp before Sunday, but it was unclear whether all had tried to flee, the security source said.
|The refugee camp was all but|
destroyed in the fighting [AFP]
The fighting has been Lebanon's worst internal violence since the 1975-1990 civil war, killing more than 300 people.
Five soldiers were also killed on Sunday, raising the army death toll to 157. At least 131 Fatah al-Islam fighters and 42 civilians have been killed.
Khodr said some army sources had told her that Shaker al-Abssi, Fatah al-Islam's leader, may have escaped during the fighting.
"Army sources say that Shaker al-Abssi has managed to escape and that eight other Fatah al-Islam fighters are on the run," she said.
"Some sources say the fighters wore army uniform, launched an attack and maybe diverted the army [during which time] the leadership managed to escape."
However, Khodr also said that other sources from the Lebanese army told her al-Abssi had been killed during the battles.
Sunday's clashes were sparked when fighters from outside the camp drove up to an army checkpoint on the eastern edge of the camp and fired at soldiers, along with fighters inside, an army source said.
Fighters also attacked another checkpoint at the southern edge of the camp.
Security forces launched a search operation and the area around the camp was cordoned off.
The road that links Tripoli to Syria was closed to traffic and army checkpoints were set up on other roads throughout the region, including the main highway to Beirut, Lebanon's capital.
Khodr, said that the checkpoints were stationed every 10 to 12 kilometres along the Beirut-Tripoli highway.
A security source said the army was concentrating its search in Ayun al-Samak, a village about 5km east of Nahr al-Bared.