"We now have an intense armed conflict raging in the streets, people are cowering in their homes, too terrified to move," he said.
Some civilians have managed to leave. Unrwa confirmed that 94 civilians, including 43 women and 20 children, had escaped and been given humanitarian support.
The Palestine Liberation Organization (PLO) in Damascus told the BBC that hundreds more had fled from this area of Damascus over the past two days.
A PLO spokesman said that two exits have been opened in the camp and that a rescue operation was being coordinated with the Syrian government and Palestinian factions inside Yarmouk.
Palestinian militiamen opposed to the Syrian government are thought to be leading the fight against IS militants in the camp, along with some Free Syrian Army fighters.
Does anyone actually know who's on their side and who isn't?
IS gunmen took over large areas of the camp on 1 April, in the group's first major attack near the heart of the Syrian capital.
According to Reuters news agency, IS posted photos of its fighters inside Yarmouk on Sunday.
|Relief workers unload aid parcels to be distributed at the Palestinian refugee |
camp of Yarmouk, in Damascus on 11 March 2015. The fighting has made it
extremely difficult for aid agencies to continue delivering supplies to Yarmouk
The battle between forces loyal to President Bashar al-Assad, rebels opposed to his rule and jihadist militants from Islamic State has also driven more than 11 million people from their homes.
Yarmouk was first built for Palestinians fleeing a different conflict, the 1948 Arab-Israeli war.
Before the Syrian civil war began, it had more than 150,000 refugees living there and had its own mosques, schools and public buildings.
But since 2012, the camp has been besieged by fighting between Syrian government troops and rebel forces.
Residents have little access to clean water, food supplies and electricity.
The few health facilities that there were in the camp have now also been engulfed in the conflict with IS.
For most of my readers, it may seem like a strange thing to ask you to pray for Palestinians; nevertheless, I'm asking you to pray for these terrified people in this utterly insane war.