Hatem al-Dimashqi, an activist based in an area just south of Damascus, said the Yarmouk camp witnessed clashes and shelling today.
Chris Gunness, a spokesman for the UN agency that supports Palestinian refugees known as UNRWA, said it has not been able to send food or convoys into the camp since the current round of fighting started.
He said: “That means that there is no food, there is no water and there is very little medicine.”
Islamic State militants stormed the camp on Wednesday, marking the extremist group’s deepest foray yet into Damascus.
Up to 18,00 civilians, including many children, are now thought to be trapped there.