Lebanese Army soldiers, supported by helicopter gunships and tanks, took the fight house to house against al Qaeda-inspired militants in a Palestinian refugee camp.
The army reportedly has control over large parts of the Nahr el-Bared camp near Tripoli, but the progress is coming at a cost.
Three Lebanese soldiers were killed and five were wounded in the fighting with Fatah Islam on Saturday, bringing the military death toll to five in the latest flurry of fighting after the new campaign was launched Friday.
Since May 20, when the conflict first began, 37 soldiers have been killed, along with at least 20 civilians and about 60 militants who were killed before the Friday offensive began.
However, journalists are being kept away from the fighting and so death tolls are difficult to independently confirm.
Lebanon's Prime Minister Fuad Saniora said about 250 members of Fatah Islam remain in the camp.
Deputy Fatah Islam leader Abu Hureira acknowledged that the militants had abandoned some positions in the northern end of the camp as part of a "tactical" withdrawal, but he said morale was high and the militants would never surrender.
Hureira also denied reports that he and Shaker Youssef al-Absi, the leader of the movement, were wounded.
Security officials claimed the majority of their work has been completed, and the military is now attempting to "mop up" pockets of resistance on the outskirts of the camp.
Officials, speaking to The Associated Press on condition of anonymity, said the camp and surrounding areas are now divided into three zones. One is under the control of the military; a second is held by militants; and a third is controlled by civilians and Palestinian guerrilla factions that are refusing to shelter the militants.
The U.S. and several Arab countries have sent ammunition and other military supplies to boost the Lebanese army's ability to combat the militants.
While an estimated 20,000 civilians have fled since the conflict began, thousands more remain in the camp.
The fighting meant humanitarian efforts had to be put on hold.
"Right now, we are waiting outside the Nahr el-Bared camp to assist the wounded people who are still inside the camp, and depending on the security situation, as soon as we can we will go inside to take care of the wounded and transfer them to hospital," said Virginia de la Guardia of the International Red Cross.
The Nahr el-Bared camp, like the 11 other Palestinian refugee camps in Lebanon, has traditionally been off limits to the military under a nearly 40-year-old agreement that allows them to govern their own affairs.
With a report from CTV's Denelle Balfour and files from The Associated Press
