For some, the journey begins with help from the Free Syrian Army, a Western-aligned loose coalition of rebels who are fighting Mr. Assad’s government, and from international coordinating bodies in the area. Spirited across the frontier into the Israeli-held Golan Heights, the patients and their relatives pass into the hands of the Israeli military.

The 5-year-old’s grandfather, a farmer, said life in wartime was like “living in a whirlpool.” When the rebellion against Mr. Assad first started, he said, “It was us against Bashar, and we had a chance of winning.” Now, he said, “the whole world is involved,” but he asked why America was not coming to the rescue.

About five weeks ago, he recalled, he had been working his land when he learned that his grandchildren had been hurt in a rocket attack. He had heard about the Israeli medical care and, ignoring the political risks, worked to bring his granddaughter here.

“When there is peace, I will raise an Israeli flag on the roof of my house,” he said.

The war has eroded once-impervious psychological barriers on both sides. This month, an Israeli aid drive led by volunteers from the Working and Studying Youth movement, Israeli Flying Aid and other local organizations collected about 20,000 items — mainly jackets, blankets and sleeping bags — to be transferred to Syrian refugees. Donors were asked to remove all Israeli labels. Barak Sella of Working and Studying Youth said there were plans to establish a website for dialogue between Israeli and Syrian youths.

A wounded mother of six, who had been at the hospital in Nahariya with two wounded daughters for nearly six weeks, said, “I grew up hearing that Israel was an enemy country and that if you met an Israeli he would kill you.”

The mother, 31, said she had been on the roof of her home with her children and a nephew as snow began when a rocket struck. She said she did not remember what happened afterward. When she awoke in the hospital, she said, “I was very, very afraid, but I tried not to show that to the staff.”

Her left leg was amputated below the knee. One daughter, 6, was recovering from shrapnel injuries. The other, 3, had lost an eye and suffered damaged lungs and a mangled arm.