Security sources said the Lebanese army was in the final phase of its campaign to defeat Fatah al-Islam and exert its control over Nahr al-Bared camp after 10 weeks of fighting that has killed at least 250 people.
"We are in the final phase of the army's operation but some of the fiercest fighting could still be ahead of us," one source said.
The army said in a statement it was doing everything possible to allow scores of civilians to leave the camp but that the fighters were stopping their families from leaving.
"The army's leadership ... reiterates its call on the gunmen to allow their family members to leave and holds them responsible for what might happen to them if they refuse," it said.
Lebanese sources estimate the number of Fatah al-Islam family members to be around 40 while Palestinian sources say the number is double that.
Fatah al-Islam, which split from a Syrian-backed Palestinian faction last year, has Lebanese, Palestinians and other Arabs in its ranks, including some who have fought in Iraq. It says it supports al Qaeda's ideas, but has no direct links with it.
The conflict has further undermined stability in Lebanon, already crippled by a prolonged political crisis and shaken by bombings that have killed six UN peacekeepers and two anti-Syrian parliamentarians in the past eight months.
More than 85 Fatah al-Islam fighters and 41 civilians have also been killed, while 65 members of the group have been detained and charged with terrorism, a charge carrying the death penalty.