Sporadic gunbattles flared overnight between Lebanese troops and militants in the Nahr al-Bared Palestinian refugee camp.
Efforts had been under way to reach a negotiated solution to what has become the worst internal strife since Lebanon's civil war.
Soldiers remain on full alert around the camp, which is the stronghold of the Fatah al-Islam group.
Fear is mounting for the fate of refugees still inside who failed to take advantage of a lull in the fighting and flee.
Lebanese troops encircled the camp last Sunday, when fighting broke out with the small Fatah al-Islam militia that has now killed 78 people, forced thousands to flee and trapped thousands more in unbearable conditions.
About two thirds of Nahr al-Bared's estimated 31,000 residents have fled, sometimes under sniper fire. But no civilians have been reported as leaving since yesterday.
Meanwhile, Lebanon has given Palestinian factions until the middle of the week to negotiate a peaceful end to deadly fighting between the army and Islamist militants, a government source said.
The negotiations involve handing over wanted fighters from the Fatah al-Islam extremist group for trial over attacks against the Lebanese armed forces since last Sunday.
The parties negotiating a possible solution are the main Palestinian factions in Lebanon including Fatah, the Islamic group Hamas and the Democratic Front for the Liberation of Palestine (DFLP).
Led by a Palestinian, Fatah Al-Islam is made up of a few hundred Islamist extremists of various Arab nationalities and is said to be inspired by the Al-Qaeda network of Osama bin Laden.
Under a longstanding arrangement, the 12 Palestinian refugee camps in Lebanon remain outside the control of the government and in the hands of armed Palestinian factions.
