It is a delicate issue for aid organizations. The Syrian government has long insisted that organizations wanting to work in government-held areas cannot work in rebel-held territory. It threw out one large aid group, Mercy Corps, in 2014, for doing so. Aid workers say that such restrictions violate humanitarian principles, and that they must be allowed to work in areas where needs are greatest.

Representatives of six aid groups spoke about the choices they have been weighing in recent weeks — all on condition of anonymity in an effort not to doom their chances of obtaining government authorization.

All the representatives insisted that it was essential to continue cross-border operations because the only other way to reach those in need is to cross front lines, from government to rebel-held territory, and Damascus has consistently put up obstacles to cross-line convoys. In report after report, the United Nations has documented bureaucratic delays and the removal of goods from humanitarian convoys, including medicines and medical supplies.

The bulk of United Nations aid to Syria is delivered to government-controlled areas, with various agencies providing food, medical care and school supplies — even garbage removal in some newly reclaimed areas — for 2.8 million Syrians. An additional 800,000 Syrians received United Nations aid through cross-border convoys in November. “This sustained assistance is essential for those in need,” Mr. Lowcock said.