"From outside 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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Witnesses said Fatah al-Islam fighters were firing back on army positions.
At least eight civilians were killed and 20 wounded on Monday in Lebanese army shelling, Palestinian sources inside the camp said.
Ghassan bin Jiddo, Al Jazeera's Beirut bureau chief, said a Palestinian delegation had contacted the Lebanese government to bring about a ceasefire.
However, Zeina Khodr, Al Jazeera's correspondent in Tripoli, reported on Monday afternoon that Lebanese army shelling and gunfights around the camp had escalated.
Abu Salim, a spokesman for Fatah al-Islam, issued an ultimatum to the Lebanese military on Monday, saying the group would escalate the battle and take it "outside" the camp if the Lebanese military did not back down.
At least 50 people died in fighting on Sunday between the Lebanese military and Fatah al-Islam fighters, but the exact toll could not be verified due to the lack of access to the camp.
Police said the night after Sunday's day-long gun battles had been relatively calm.
Palestinian representatives have called for medical aid be sent to the camp.
There are reports that water tanks in the camp have been destroyed by Lebanese army shelling.
Abu Hisham Laila, an official of the Popular Front for the Liberation of Palestine, speaking to Al Jazeera from inside the camp, called the Lebanese bombing of the camp "indiscriminate".
"All residents have stayed at home, taking shelter in lower floors," he said.
"We want ambulances to be allowed into the camp to transfer the civilian casualties. We also want fire brigades to enter the camp and put off the fire in many buildings."
Zeina Khodr, reporting for Al Jazeera from close to the Nahr al-Bared camp, said: "The camp is virtually sealed off. Palestinians inside are telling us there are scores of civilian wounded." Links to al-Qaeda
Fighting broke out between the army and Fatah al-Islam on Sunday morning after security forces raided homes in the Lebanese town of Tripoli to arrest suspects of a bank robbery.
At least three members of Fatah al-Islam, which has been accused of having links to al-Qaeda and Syrian intelligence, were killed after the army stormed a building in Tripoli in which they were hiding.
Fighting at the camp, where Fatah al-Islam has its headquarters, came in response to the raid in Tripoli by the Lebanese military.
A judicial source said on Monday that one of the fighters killed in Sunday's fighting was wanted by Lebanon for involvement in a plot to bomb two trains in Germany last year.
Saddam al-Hajj Deeb, a Lebanese citizen, was one of five men charged with attempted mass murder.
Deeb was on the run and being tried in absentia.
Fouad Siniora, Lebanon's prime minister, accused the group of trying to destabilise the country and called on the people of Lebanon to "join ranks behind the army and Lebanese security forces".
Fatah al-Islam's spokesman told Al Jazeera that the group was acting in self defence and had been made a "scapegoat".
The organisation has denied links to al-Qaeda and charges that it carried out bus bombings that left three people dead in a Christian area north of Beirut in February.
The group accused the government of trying to pave the way for an offensive against Palestinian refugee camps in Lebanon.
Also on Sunday, an explosion near a shopping centre in Beirut, Lebanon's capital, killed a 63-year-old woman and injured 10 people.
The blast, across the street from the ABC shopping centre, occurred shortly before midnight (21:00 GMT) in Ashrafieh, an upmarket and largely Christian neighbourhood, leaving a crater 1.5m deep and 3m wide in the road.
The blast appeared to have come from explosives placed inside a parked vehicle.