Zeina Khodr, Al Jazeera's correspondent in Lebanon, 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.
The 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.
The source said three people who were in the car that attacked the checkpoint were killed.
Fighters also attacked another checkpoint at the southern edge of the camp. Army troops detained nine fighters during the clashes.
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 ten to twelve kilometres along the Beirut-Tripoli highway.
Search under way
The army source said the army was concentrating its search in Ayun al-Samak, a village about five kilometres east of Nahr al-Bared.
Earlier this week, the army refused to allow wounded Fatah al-Islam fighters to be evacuated from the camp.
The army has called for the unconditional surrender of the estimated 60 remaining fighters in the camp.
On Saturday, army troops seized the homes of Shaker al-Abssi and Abu Hureira, the Sunni group's senior leaders.
Abu Hureira, who was killed by the army in July, was buried on Saturday in a cemetery near his parents' home in Tripoli, one of Abu Hureira's brothers said on condition of anonymity.
At least 200 people, including 155 soldiers, have died in fighting in and around the refugee camp, in Lebanon's most deadly internal violence since the end of civil war in 1990.