'Self-defence'
Elias Murr, the Lebanese defence minister, said the group had two choices: "Surrender or the army will take the military option."
Earlier, Fouad Siniora, the prime minister, vowed to wipe out the group, raising prospects of a bloody battle if troops stormed the camp, or lay siege until the fighters surrendered.
Speaking to Al Jazeera after Thursday evening's clashes with the Lebanese army, Fatah-al Islam's official spokesman said the group was only "exercising self-defence".
"It has never crossed our minds to leave or surrender ourselves in any manner," Abu Salim said.
"We keep saying - those who fire explosives at every corner of the refugee camp, were to be held responsible for the loss of civilian life.
"We used to protect civilian lives when we unilaterally took the initiative to a ceasefire, while we faced gunfire everyday."
Tough line
Thousands of people have fled the camp after a lull in fighting between the army and Fatah al-Islam in which 69 people died.
Siniora took a tough line on Fatah al-Islam in a televised speech to the nation on Thursday, saying: "We will put an end to the terrorist phenomenon without hesitation."
He said Fatah al-Islam is "attempting to ride on the suffering and the struggle of the Palestinian people".
Siniora told Palestinian refugees in his TV address: "You are our brothers.
"We share with you the bad times before the good ones."
Bomb blast
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"From outside Lebanon it's very easy to condemn the Lebanese army and government for what they are doing against Fatah al-Islam"
Rabih, Mansourieh El Metn, Lebanon
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Lebanon was also hit by its third bomb attack in four days on Wednesday night.
One person was killed when a bomb in a suitcase ripped through a building in the eastern town of Aley.
The blast was the third in the Beirut area in four days, and follows a spate of attacks over the past two years against prominent critics of Lebanon's former power broker Syria.
Walid Jumblatt, the Druze leader and a key figure in the anti-Syrian parliamentary majority, pointed the finger at Damascus.
He said it was trying to block a UN resolution due to set up a tribunal to try suspects in the 2005 killing of former Rafiq al-Hariri, the former Lebanese prime minister.
Syria has denied any involvement in the attacks.
Thousands of people camped in makeshift accommodation in northern Lebanon overnight after taking advantage of the two-day truce.
The International Committee of the Red Cross [ICRC] said on Wednesday that between 13,000 and 15,000 refugees had left Nahr al-Bared since the fighting stopped, about half the population of the camp.
Early on Thursday, families continued to stream out of the besieged camp on foot, under the watchful eyes of soldiers posted outside.
Relief agencies are hoping to get more aid to those still inside the once densely populated camp, which has been battered by army shelling.