"All high buildings which were manned by the militants of Fatah al-Islam are now in the hands of the Lebanese army," a high-ranking army source said.
"We are moving in the area cautiously because of the mines, but most of the positions which used to be manned by the extremists are destroyed and are now in our hands," the source said.
"All high-rise buildings which were used by the militants as sniping bases and to launch attacks against our troops are now in the hands of the Lebanese army and you can see Lebanese flags on top of them," he added.
Wednesday saw an easing in the intensity of fighting and only a few shells were heard across the Palestinian refugee camp.
So far at least 141 people were killed, including 74 Lebanese soldiers, in the violence that started May 20.
Army commander Michel Suleiman was quoted as saying that the fighting will end in the coming few days.
As the battle with the Fatah al-Islam group eased off, Palestinian mediators gave indications that a cease-fire deal with the militants was a possibility.
According to a Palestinian Muslim cleric who has been acting as mediator, the deal would include a cease-fire, to be followed by the militants' disarmament.
Sheikh Mohammed Haj told Deutsche Presse-Agentur dpa that "very positive" meetings with Fatah al-Islam leaders were held inside the camp, but he would not give details before a scheduled meeting with the army command on Wednesday.
He added that a force made of Palestinian factions would be deployed at the outskirts of the camp to ensure the safety of some 2,000 Palestinians still inside the camp and that the details were being discussed with the army command.
Meanwhile, Abu Imad Rifai, a representative of the Palestinian militant group Islamic Jihad, told the Hezbollah-run al-Manar television that progress was made after Fatah al-Islam "opened the doors for a solution" and accepted the proposal to "dissolve."
The army had said it will crush Fatah al-Islam no matter how much it took, while the militants had pledged to fight to the death rather than comply with the army's request to surrender.
The fighting in Nahr el-Bared comes amid a serious political deadlock and standoff between the Western-backed government of Lebanese Prime Minister Fouad Seniora and the opposition led by the militant Hezbollah group.
Fatah al-Islam emerged late last year after its leader, Shaker al-Abssi and 200 fighters split from the pro-Syrian Palestinian faction Fatah al-Intifada (Uprising).
Lebanon's Western-backed government says Fatah al-Islam is linked to Syrian intelligence, a charge denied by Damascus and the group itself. Abssi has said he supports the ideas of al-Qaeda terrorists but has no organisational ties to Osama bin Laden's network.
Most of the camps 40,000 Palestinian residents have fled the camp to the nearby Bedawi camp. Only 2,000 refugees remain inside. dpa wh mga
- Deutsche Presse Agentur
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