BEIRUT (AP) — International aid organizations sounded the alarm Wednesday for the fate of thousands of desperate Syrians fleeing the onslaught of President Bashar Assad's forces in southwestern Syria, urging neighboring countries to take them in.

The calls come as Jordan has said it will not open its borders to the Syrians, asking instead the United Nations to provide them with security within their home country. The U.N., meanwhile, said that up to 50,000 have already been displaced by the fighting — including 20,000 children and their families, in just three days.

Jordan, the small neighboring country with a population of over 9 million, has 660,000 registered Syrian refugees and estimates that many more live in the kingdom without having registered. Israel has not commented of the wave of displacement, although Syrian residents said many of the displaced have sought refuge near the frontier with the Israeli-occupied Golan Heights.

"We are receiving reports about people fleeing as the front lines shift," Robert Mardini, the regional chief for the International Committee of the Red Cross. "We ask those fighting and neighboring countries to facilitate civilians' access to safety and essential services, including life-saving medical care. Civilians should, as always, have options to flee the violence and seek refuge and protection."

The Norwegian Refugee Council specifically urged Jordan to take in thousands of Syrians, saying they have "nowhere else to turn" as they flee Assad's forces, which began their offensive in southern Daraa province on June 19, shattering a year-long truce.

The aid group, however, cautioned that Jordan, which already hosts hundreds of thousands of Syrians, cannot be expected to shoulder the burden alone.

The NRC also said the international community must "offer substantial support" and added that aid groups are ready to help potential new arrivals settle in Jordan's Azraq camp, which it estimates can house 80,000 more people.

"The situation on the ground in Syria seems to be extremely worrying," Daniel Gorevan of the NRC told The Associated Press. The NRC estimates that 70,000 have fled the violence, while thousands of families are being pushed further south "where they eventually" will run into Jordan's closed border.

"Jordan has done so much over the last years to accommodate so many Syrian refugees and we are calling for the international community to support Jordan to make this division to host these refugees," Gorevan said.

The strategic southern region in Syria borders Jordan and the Israeli-occupied Golan Heights. The Syrian government troops are seeking to dislodge rebels who have been in the area for years, and gain control of the commercial border crossing with Jordan.

The executive director of the U.N children's agency UNICEF, Henrietta H. Fore, said Wednesday that violence in southern Syria has displacing thousands of children in just three days and killed at least four.

"Horror knows no limit in Syria" she said in a statement. "Those wishing to flee should be allowed to reach safe havens, away from the sights and sounds of war ... The children of Syria have lived through unacceptable suffering. This cannot become the new normal."

Associated Press writers Fares Akram and Karin Laub in Amman, Jordan, contributed to this report.