The latest battle started at dawn. Medical sources from inside the camp were calling for the fighting to stop because they said there were dead and wounded on the streets.
Television footage showed a plume of dark smoke rising from inside the camp, home to 40,000 Palestinian refugees.
"We can hear very intense shelling, it's constant," said a Reuters witness at the scene.
At least 20 militants, 32 soldiers and 27 civilians have been killed since fighting between the army and Fatah al-Islam fighters erupted early on Sunday, making it Lebanon's worst internal violence since the 1975-1990 civil war.
Fifty-five soldiers have also been wounded.
On Monday, Palestinians in the camp said thousands had fled their homes on the edges of Nahr al-Bared, where fighting was most intense, to shelter deeper inside the camp. More than 150 people had been wounded and dozens of homes destroyed, Palestinian sources said.
Prime Minister Fouad Siniora's government on Monday stressed the need "to put an end to" Fatah al-Islam, a Sunni Muslim group which emerged late last year. It has only a few hundred fighters and scant political support in Lebanon.
Based in Nahr al-Bared, the group is thought to have links with jihadist factions in other Palestinian camps.
- Reuters - Thomson Reuters Foundation
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