The Lebanese army began operations against Fatah al-Islam in May in the wake of an attack on soldiers in Tripoli.
Security sources told Reuters news agency that some of the explosions on Friday were caused by soldiers blowing up booby-trapped buildings and mines.
Murr said many of the remaining fighters had withdrawn to civilian areas deep inside Nahr al-Bared and the army would continue its siege until they gave themselves up.
"The Palestinian refugees are not being treated properly by Lebanon"
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He said Shaker al-Abssi, Fatah al-Islam's leader, was unaccounted for, along with his deputy Abu Hureira.
"It's not good enough to say Abssi was killed. If he is dead, give us the body."
Zeina Khodr, Al Jazeera's correspondent in northern Lebanon, said: "From where we are standing we are not hearing any resistance, it is just the Lebanese army pounding positions and detonating bombs.
"It is very early to say that this is a victory, very early to say that this crisis is over."
Mohammed al-Hajj, spokesman for a group of Palestinian religious leaders negotiating a truce, said that Fatah al-Islam had said it would respect a ceasefire.
"I have been in contact with their spokesman Shahin Shahin, and they are ready to respect a truce," he said.
The mediators were scheduled to meet Saudi diplomats later in the day to discuss the fate of Saudi nationals who had joined Fatah al-Islam, and ways of funding reconstruction in the camp.
Fighting soon moved to Nahr al-Bared, home to at least 30,000 Palestinian refugees.
Thousands of civilians in the camp fled amid fierce fighting between the army and Fatah al-Islam fighters entrenched in the camp.
At least 75 soldiers and 60 Fatah al-Islam fighters, as well as 20 civilians, are understood to have been killed in the weeks of fighting.
The Lebanese army has largely shelled the camp from its perimeter, observing a decades-old deal that prevents the army from entering Palestinian refugee camps.
Source: Al Jazeera and agencies