Jordan, meanwhile, closed its only functioning border crossing with Syria, following heavy clashes on the Syrian side between rebels and government forces.
Islamic State fighters, who control large swaths of territory in northern Syria, entered the Yarmouk camp from the nearby Hajar Aswad neighborhood.
The Britain-based Syrian Observatory for Human Rights said the IS group took control of large parts of the camp. If they gain full control, they can potentially threaten the heart of the capital.
Anwar Raja, the spokesman for the pro-Assad Popular Front for the Liberation of Palestine -- General Command, said that IS fighters had been based in the Hajar Aswad neighborhood for months.
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He said today's push into the camp showed coordination between IS and a rival group, the Nusra Front, al-Qaida's branch in Syria.
"The Nusra Front opened the road for them in order to infiltrate the camp and several hours ago they entered Yarmouk," Raja said by telephone.
Yarmouk, a Palestinian refugee camp in southern Damascus, has been under government siege for nearly two years.
UN aid workers have been sending food parcels into the camp, where thousands of civilians remain trapped and in desperate need of food and medicine.
The camp had witnessed fighting in the past between government forces and militants who control much of the camp.
The UN agency that supports Palestinians, known as UNRWA, said it was extremely concerned about the safety and protection of the Syrian and Palestinian civilians in Yarmouk, particularly the children.
It demanded "an end to the fighting and a return to conditions that will enable its staff to support and assist Yarmouk's civilians.