Smoke billowed from breeze-block buildings inside the camp, television footage showed.
The conflict at the camp is Lebanon's worst internal fighting since the 1975-1990 civil war.
So far it has killed at least 83 people, including 34 soldiers, 29 Fatah al-Islam fighters and 20 civilians.
A Lebanese soldier was killed and three others were wounded in fighting on Thursday.
The government is demanding that the fighters surrender, and the authorities have already charged 20 captured members of the group with "terrorism". The charges carry the death penalty.
Lebanon's government has given Palestinian leaders in Lebanon a chance to find a way out of the two-week stand-off because it fears the fighting could spread to other refugee camps.
Abbas Zaki, the Palestine Liberation Organisation (PLO) representative in Lebanon, urged the Fatah al-Islam fighters to surrender.
More than 25,000 of the Nahr al-Bared's 40,000 Palestinians have fled to the nearby Beddawi camp, where humanitarian organisations have been carrying out relief work.
Members of Lebanon's anti-Syrian cabinet have described Fatah al-Islam as a tool of Syrian intelligence, though Damascus denies any links to the group and says its leader, Shaker al-Abssi, is on Syria's wanted list.
Al-Abssi has said he follows al-Qaeda's ideology, but has no direct links to Osama bin Laden's network. Many of his estimated 300 gunmen are believed to have fought in Iraq.
Lebanese authorities say Fatah al-Islam includes Arabs from Saudi Arabia, Algeria, Tunisia, Syria and Lebanon.