Warplanes have bombarded a district housing Palestinian refugees in the Syrian capital for the first time since the anti-regime uprising began.
"We also call on the international community to take immediate action to provide protection to our people in Syria," Abbas said, adding that the Palestinians were "not involved" in the conflict.
As the Syrians, Palestinians have been divided over the uprising, with some taking up arms against the regime and others fighting to defend it.
Yarmouk is part of an arc sweeping from the east to southwest of the Syrian capital where government troops have been trying for several weeks to push back rebels.
Activists also reported bombardment of the nearby districts of Hajar al-Aswad and Assali.
Meanwhile, Alaeddin al-Sabbagh, former head of public relations in the Syrian intelligence, announced his defection while speaking to Al Jazeera.
He said he had been in touch with rebels for some time and that they knew he was serving the revolution while he was in office. He called Assad's regime a "clinically dead" one.
The opposition says more than 40,000 people have been killed since the uprising started in March last year and gradually turned into a civil war. Hundreds of thousands have fled to neighboring countries and many more have been displaced internally.
PHOTO CAPTION
Palestinian children play at al-Bassel swimming pool in the heart of the Palestinian refugee camp of Yarmuk on the outskirts of Damascus on August 29, 2007.
Aljazeera