Jordan houses Syrian refugees in a camp near the border, but officially bars any Palestinians from entering the country. Lebanon, on the other hand, has kept an open-door policy to anyone fleeing the Syrian conflict, despite the country’s sectarian tensions and the specific fears about Palestinian refugees.

Until now, Lebanon has kept its borders open to all refugees, and has not restricted where they can move. In recent weeks, politicians have bandied about the idea of establishing transit camps for Syrians crossing the border, but no consensus has emerged and the government is hamstrung by the prime minister’s resignation in March. The current caretaker government is struggling to pave a path toward elections, originally scheduled for June, and is unlikely to take any action at all on the questions of refugees from Syria and the Lebanese government’s official position of neutrality in the conflict.

Humanitarian agencies have struggled to keep up with the Syrian refugee crisis and are still waiting for pledged funds to arrive. The relief and works agency operates schools, clinics and aid distribution sites throughout the region, so Palestinians fleeing the war in Syria have it better than others; they can almost immediately continue drawing benefits, enroll their children in agency schools and obtain health care. In contrast, regular Syrian refugees face six-month waits just to register with the Office of the United Nations High Commissioner for Refugees, which handles all non-Palestinian refugees.

Funds have been scarce. The relief and works agency has received about 60 percent of the financing it requested when it expected a much smaller number of refugees than it is already managing. It has given irregular cash payments of about $100 to Palestinian families who have fled to Lebanon. Other refugee agencies have received less than half of what they need.

If fighting intensifies in Damascus, the Syrian capital, Mr. Grandi said, the trickle of fleeing Palestinians could quickly become a tide. But the half a million Palestininans in Syria who might join the exodus if the capital falls into chaos would be just one part of a greater humanitarian catastrophe.

If United Nations predictions of an additional two million to three million displaced people in Syria this year materialize, Mr. Grandi said, Syria’s neighbors, and international humanitarian agencies, would simply crumble.

“We need to keep sounding this warning,” Mr. Grandi said. “A political solution needs to be found.”