AMMAN, Jordan — Islamic State militants have seized most of a sprawling Palestinian refugee district in the southern part of the Syrian capital, Damascus, an area that has been under siege and bombardment for nearly two years already, according to Palestinian and United Nations officials and residents.

The officials called for quick action by international organizations, the Syrian government and all armed groups to head off an unfolding catastrophe. Reports of killings and even beheadings were beginning to circulate on Saturday, worsening what is already a longstanding humanitarian nightmare for the 18,000 residents of the Yarmouk refugee camp.

By seizing much of the camp, the Islamic State terrorist group, also known as ISIS or ISIL, made its greatest inroads yet into Damascus, a significant step for a group that rose largely in the northern and eastern provinces of Syria, far from the capital. Yet at the same time, the move suggests that as the Islamic State loses ground in Iraq and northeastern Syria, the most daring response it could muster on the ground was to attack one of the most vulnerable populations in Syria.

Most of all, the attack was a perverse answer to the question of how life in Yarmouk could get worse. Many residents’ very presence there is a scar from a previous war; they are descended from Palestinians who fled or were driven from their homes in the 1948 war over Israel’s founding.