BEIRUT -- Hundreds of residents of a Palestinian refugee camp in the Syrian capital Damascus fled Sunday amid shelling by government forces and clashes between Islamic State fighters and Palestinian militants, activists said.

An activist based in an area just south of Damascus, Hatem al-Dimashqi, said many residents started fleeing the Yarmouk camp after midnight as the fighting let up. The camp has been subjected to intense shelling and airstrikes by the government.

The Britain-based Syrian Observatory for Human Rights and al-Dimashqi said those who fled the camp have reached the southern Damascus suburbs of Yalda, Babila and Beit Sahem, which are under rebel control.

Al-Dimashqi and Syrian state TV said as many as 2,000 people have left the camp. The activist said that many of those who fled the camp are staying in schools or abandoned homes.

Palestinian President Mahmoud Abbas said in Ramallah that residents of Yarmouk have been victimized by Syria's civil war. Government forces and different rebel factions are clashing and "we pay the price," he said.

He added that the Palestine Liberation Organization in Damascus has formed a "cell to handle this tragedy and they are trying to work it out with the least losses." Abbas said: "We are in touch with our brothers there to find a way out and protect our people."

Islamic State militants stormed the camp on Wednesday, marking the extremist group's deepest foray yet into the capital. Palestinian officials and Syrian activists said they were working with rivals from the al-Qaida affiliate in Syria, the Nusra Front. The two groups have fought bloody battles against each other in other parts of Syria, but appear to be co-operating in the attack on Yarmouk.

The Nusra Front said in a statement Sunday that it is not participating in the battles and is taking a neutral stance. The statement added that Nusra opened its offices and welcomed all those who don't want to take part in the fighting and gave them refuge.

The Observatory said the fighting has killed 26 people since the clashes first broke out.

In Gaza, several hundred supporters of the ruling Hamas group staged a march late Sunday in the Jebaliya refugee camp to protest the Islamic State group's takeover of parts of Yarmouk.

"Palestinian blood is not cheap," Mohammed Abu Askar, a local Hamas leader, told the crowd, threatening revenge for the Islamic State incursion into Yarmouk.

In Damascus, Anwar Raja, the spokesman for Damsascus-based Popular Front for the Liberation of Palestine -- General Command, which supports embattled Syrian President Bashar Assad, said several pro-Assad factions have united to defend the camp. He said more than 100 civilians have been either killed or kidnapped by the IS fighters whom he said now control about half the camp, adding that the priority now is to evacuate civilians.

The United Nations says around 18,000 civilians, including a large number of children, are trapped in Yarmouk. The camp has been under government siege for nearly two years, leading to starvation and illnesses caused by lack of medical aid. The camp has also witnessed several rounds of ferocious and deadly fighting between government forces and militants.

Most of the camp's estimated 160,000 inhabitants fled in late 2012 as clashes erupted between pro- and anti-Assad Palestinian gunmen-- many to overcrowded and destitute Palestinian refugee camps in neighbouring Lebanon. Only the poorest remained behind.

Also Sunday, Lebanon's state-run National News Agency said six Lebanese truck drivers who were held by militants after they captured the Nasib border crossing point with Jordan have returned safely to Lebanon. The agency reported on Friday that 10 drivers were held by militants. The fate of the others is still unknown.