The combatants exchanged artillery shells and mortar bombs for hours overnight in the heaviest fighting in a week, witnesses said.
But the clashes tapered off in the early hours of Wednesday.
The Lebanese government has demanded that the fighters surrender.
Fatah al-Islam said they have been acting in self-defence and rejected the demand to hand over any of their fighters.
A 1969 Arab agreement stops the army from entering Lebanon's 12 Palestinian refugee camps, home to 400,000.
The government has given Palestinian leaders in Lebanon a chance to find a way out of the stand-off, as it is concerned that the refugees will see more army action at the camp as an attack on their community.
More than 25,000 of the camp's 40,000 Palestinians have fled from the fighting.
Most of the displaced refugees have flooded the nearby Badawi camp, where humanitarian organisations have been carrying out relief work.
"The Palestinian refugees are not being treated properly by Lebanon"
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More food supplies, medicine and water were sent to Nahr al-Bared, whose remaining inhabitants have no electricity or running water, witnesses said.
The prospect of a decisive military solution to the stand-off has been played down by the government in recent days because it could trigger violence at other refugee camps, even though Fatah al-Islam has little support among Palestinians.
Members of Lebanon's anti-Syrian cabinet have described Fatah al-Islam as a tool of Syrian intelligence, although Damascus denies any links to the group.
Lebanese authorities say Fatah al-Islam includes Arabs from Saudi Arabia, Algeria, Tunisia, Syria and Lebanon.