Two Lebanese soldiers died Tuesday in the ongoing battle against al-Qaida-inspired fighters in a Palestinian refugee camp in northern Lebanon as the army inched toward the militants' strongholds, officials said. Meanwhile, mediators hinted at a possible cease-fire deal with the militants holed up in the Nahr el-Bared camp on the outskirts of the port city of Tripoli. According to a Palestinian Muslim cleric who has been mediating between the authorities and the Fatah Islam fighters inside the camp, the deal would include a cease-fire, to be followed by the militants' disarmament and surrender. The cleric, Sheik Mohammed Haj, told the Associated Press he had a "very positive" meeting with Fatah Islam leaders inside the camp Monday but would not give details before a scheduled meeting with the army commander on Wednesday. He earlier told the official Lebanese news agency that the militants agreed to conditions of his Palestinian Scholars Association. Sheik Mohammed did not offer more details, but the private New TV station said the conditions also include return of refugees, takeover of the camp by other Palestinian factions and Fatah Islam's dissolution. The army had in the past said its decision to eliminate Fatah Islam was "final and irreversible." Previous mediation efforts by the cleric, who was slightly wounded during one of his trips into the camp, came up against the militants' pledge to fight to death rather than comply by the army's request that they surrender. In Tuesday's fighting at Nahr el-Bared, a barrage of six shells at a time was heard as the army pounded the camp. Black and white plumes of smoke were seen rising from inside the camp. A military official, speaking on condition of anonymity because he was not authorized to make statements to media, said a soldier was killed in battles earlier in the morning with Fatah Islam gunmen. Another security official, also requesting anonymity for the same reason, said a second soldier was killed shortly before midday by sniper fire. Tuesday's deaths brought the army's fatalities to 74 since fighting first erupted here May 20, when police raiding suspects in a bank robbery clashed with Fatah Islam in a Tripoli neighborhood. Fatah Islam - a group of Islamic militants from various Arab nationalities that built its power structure in the camp in recent months - subsequently burst out of Nahr el-Bared, attacked Lebanese army positions and ambushed soldiers, killing 27 in attacks condemned by Lebanese and Palestinians alike. At least 60 militants were killed in the early days of the fighting, with officials saying many more died later on. The militants have given a much lower death toll, but contact with them recently has not been possible. At least 20 civilians were reported killed. The army has made steady gains on the ground in recent days. On occasion, it leveled top floors of buildings to root out militant snipers, and engaged in door-to-door combat to try to break the stubborn resistance of the militants who operate from behind fortified positions and target the military with rockets and booby traps. The battle to drive the Islamic militants out has led to significant damage to parts of the camp, once home to some 30,000 Palestinian refugees. Only about 5,000 remain inside, after most residents fled to the nearby Beddawi refugee camp. With the military advancing in recent days, the militants have been retreating deeper inside Nahr el-Bared's narrow streets and residential neighborhoods, hounded by army artillery. There has been little information from inside the camp since the early days of the fighting, as Nahr el-Bared has been off limits to journalists. An amateur video obtained by Associated Press Television News on Tuesday showed major destruction in largely deserted residential neighborhoods. Debris from collapsed walls and balconies littered the narrow alleys, covered with ripped electricity wires. Shells and shrapnel holes peppered some buildings. A burnt car and a parked pickup truck with a collapsed wall resting on it lay on one deserted street. The video, taken at different periods between May 27 and June 10, showed very few residents. Six men were seen gathering around a hose to fill up cans with water. In one house, a family was sitting on the floor for a meal.