For the first time since the conflict started two weeks ago, the Lebanese military has begun targeting locations deep within the Palestinian refugee camp occupied by al Qaeda-inspired militants.

On Sunday, the third day of a stepped-up military offensive to oust the Fatah Islam members holed-up in the Nahr el-Bared camp near Tripoli, white smoke billowed from the compound.

The area had been sealed off and journalists were being kept away from the scene of the fighting.

On Sunday, Lebanese officials said one of the group's chiefs, who was known to send fighters into Iraq, was killed in the ongoing conflict.

Naim Deeb Ghali, also known as Abu Riad, was the third-in-command of the group, The Associated Press reports.

The report was confirmed by Abu Hureira, Fatah Islam's deputy commander.

On Saturday, Lebanese soldiers supported by helicopter gunships and tanks, took the fight house to house in the 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.

Four Lebanese soldiers were killed and 10 were wounded in Saturday's fighting.

Since the fighting began on May 20, 38 soldiers have been killed, along with at least 20 civilians and about 60 militants. However, recent casualties inside the camp are unknown because relief organizations haven't been allowed in since Friday.

A Fatah Islam official said two fighters had been wounded in the past two days.

Lebanon's Prime Minister Fuad Saniora said Saturday 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 Saturday 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 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 files from The Associated Press