The head of a group overseeing a contentious new aid program in the Gaza Strip resigned on Sunday, hours before the program was set to start operating, saying that he had found it impossible to perform the job independently.

Jake Wood, the executive director of Gaza Humanitarian Foundation, stepped down after reports in several news outlets, including The New York Times, raised questions about the group’s independence and its connections with Israel.

In a statement distributed by the foundation, Mr. Wood said: “It is clear that it is not possible to implement this plan while also strictly adhering to the humanitarian principles of humanity, neutrality, impartiality, and independence, which I will not abandon.”

Mr. Wood’s departure followed growing acrimony within the traditional aid sector about efforts by Israel to replace the current aid system in Gaza with one overseen by the Gaza Humanitarian Foundation, a new and untested group founded late last year. The foundation has hired private contractors, including one run by a former C.I.A. officer, to secure and distribute food from four sites in areas of southern Gaza under Israeli military control.

Aid agencies have warned of a looming famine since early March, when Israel implemented a blockade on food and fuel to Gaza. That blockade has only just begun to ease.

The project’s supporters say it will enable Palestinian civilians to access food while preventing Hamas from stealing, stockpiling and even selling it at elevated prices. Critics, including the United Nations, say it is a dangerous plan that will force civilians walk miles through Israeli military lines to find food, and likely accelerate an Israeli goal to displace people from northern to southern Gaza.