In interviews, dozens of Syrians living in rebel-held territory in the provinces of Aleppo and Idlib insisted that their towns had received no Western aid and groused about “empty promises.” Only a few most directly involved in aid distribution acknowledged recent visits from international nonprofit groups, and those with knowledge of the meetings insisted that the names of the aid groups remain confidential.

Even the Syrians most involved in the Western effort expressed frustration. “We believe we are owed an explanation over where this money is going, but every time we ask, we can’t get an answer,” said Ghassan Hitto, who runs the aid coordination arm of the Western-backed Syrian national coalition. He estimated that as much as 60 percent of the Syrian population lives outside the Assad government’s control and thus beyond the reach of most aid. It is an assessment that is impossible to confirm but feasible because of the heavy population of the rebel-controlled north.

United Nations officials acknowledge the problem. But they say they have few alternatives while the United Nations recognizes the government, which is unlikely to change as long as Russia supports Mr. Assad. “The government, whether you like it or not, is still the government,” said Jens Laerke, a spokesman for the United Nations Office for the Coordination of Humanitarian Affairs.

Among other obstructions, Mr. Assad has blocked any United Nations agencies from the shortest and safest route into rebel territory, across the opposition-controlled border with Turkey. “We do not have the government’s consent,” Mr. Laerke said. “So we cannot, as the United Nations, do that.”

To get around that ban, at least three United Nations relief convoys have crossed the battle lines to reach parts of the north, Mr. Laerke said, but it is a dangerous trip. Eight United Nations aid workers have been killed during the Syrian conflict, he said.

Image Disparities along the Syria-Turkey border are jarring. Credit... The New York Times

Mr. Laerke said that as much as 45 percent of the 1.7 million people inside Syria who have received some aid from United Nations food programs live in areas that are at least contested by the rebels. But other aid workers and international observers said those statistics vastly understated the gap.