Earlier on Saturday, Al Jazeera aired a tape featuring a speech by Fatah al-Islam's leader.
Shaker al-Abssi said: "We wish to die. We wish to die for the sake of God. If the leader is sitting at the forefront, he will set an example for his followers."
He said Fatah al-Islam would fight "the Jews, the Americans and their loyalists", an apparent reference to Lebanon's government.
On Friday, Hassan Nasrallah, secretary-general of Hezbollah, said in a televised speech that the country risked getting dragged into America's war against al-Qaeda.
He said: "The problem in the north can be solved politically and through the judiciary."
Nasrallah said accepting US help would draw more fighters into the country and potentially destabilise it.
Fuad Siniora, Lebanon's prime minister, has defended the import of military supplies from the US, saying the supplies had been offered by several countries months ago.
The US-supplied aid is a sensitive issue in Lebanon, where opposition leaders accuse the government of working to Washington's agenda.
Palestinian factions have been seeking a negotiated solution to end the siege and avert a battle between the Lebanese army and Fatah al-Islam.
'There is optimism'
Osama Hamdan, Hamas's representative in Lebanon, said that "as long as we agree on the necessity of a solution and we speak with a language of solution, then there is optimism".
Elias Murr, Lebanon's defence minister, said on Friday he was "leaving room for political negotiations", which he said must lead to the surrender of the Fatah al-Islam fighters.
He said: "If the political negotiations fail, I leave it to the military command to do what is necessary."
The UN has called for the protection of thousands of civilians trapped by the Lebanese army's siege of the camp.
About half of Nahr el-Bared's 31,000 residents fled the camp during an earlier truce, seeking shelter in the nearby Beddawi camp.