The flood has also raised fears that the refugees will import the Syrian conflict into the host countries, and destabilize already fragile borders. Like the other host nations, Turkey, which is actively supporting the Syrian opposition, was struggling to control the mass movements across its border.

In Hatay, Turkey’s southwestern province, hundreds of Syrians could be seen crossing illegally, unchecked by border guards or soldiers. Stretches of the border appeared porous and lawless. Criminal gangs thriving in the cross-border smuggling of gasoline and other goods could be seen working in broad daylight, using walkie-talkies to direct trucks in and out of Syria.

A few miles from one of the biggest smuggling centers, the Turkish border town Bes Arslan, soldiers could sometimes be seen chasing individual Syrians clambering down a hill into Turkey. In a cat-and-mouse game played out over the day, Syrians crouched behind trees and rocks, some successfully slipping into Turkey; others were caught by soldiers and sent back.

Those turned away often try again later in the day. As soon as darkness fell, hundreds of Syrians began pouring out of Bes Arslan onto the highway, where relatives and taxi drivers were waiting. Slipping in and out of the headlights, they stuffed large suitcases into vehicles that quickly took them deeper into Turkey.

One weeping woman was ushered into the back seat of a car as the driver and others took care of her luggage and five children. Her baby, who had been sitting on the asphalt, was finally put inside, and the car whisked the family away. Her husband had died in a bombing earlier that day during the family’s flight.

“She had to leave his body behind in Syria,” said one of the men who had helped her with her luggage. “The driver is taking her into town for free.”

Rising Frustration

Saher Hardan, another squatter in Kilis, fled Syria two years ago with her children. With the money she earned from selling a modest piece of land, the family lived in a $75-a-month apartment here until recently. Now out of money, the Hardans sleep inside a tent with their neatly stacked belongings. A framed portrait of Ms. Hardan’s husband — a former school janitor who fought for the Western-backed Free Syrian Army and was killed, “torn into pieces” in an explosion — sat prominently in the middle of the tent.