"The situation in Yarmouk is an affront to the humanity of all of us, a source of universal shame," U.N. Relief and Works Agency (UNRWA) spokesman Chris Gunness said.
"Yarmouk is a test, a challenge for the international community. We must not fail. The credibility of the international system itself is at stake," he said.
The Syrian Observatory for Human Rights, which monitors the conflict from Britain, said Syrian air force jet bombed the camp on Saturday.
The Islamic State on Wednesday launched an attack on other groups of fighters in Yarmouk, in particular Aknaf Beit al-Maqdis, an anti-Assad militia of Syrians and Palestinians from the camp.
Islamic State supporters posted photos on social media of the severed heads of two men they said had been beheaded after fighting for Aknaf Beit al-Maqdis.