GAZA CITY—Hidden deep below the headquarters of the United Nations' aid agency for Palestinians here is a Hamas complex with rows of computer servers that Israel's armed forces say served as an important communications center and intelligence hub for the Islamist militant group.

Part of a warren of tunnels and subterranean chambers carved from the Gaza Strip's sandy soil, the compound below the United Nations Relief and Works Agency buildings in Gaza City appears to have run on electricity drawn from the U.N.'s power supply, Israeli officials said.