WASHINGTON—The Trump administration on Friday asked for more time to decide whether to shield documents concerning allegations of official Saudi involvement in the Sept. 11, 2001, terrorist attacks, a sign that top Justice Department officials are struggling how to handle demands from victims’ families to release the information.

The families are seeking the information as part of a lawsuit against Saudi Arabia that accuses its government of helping coordinate the 2001 attacks. The U.S. government’s pending decision comes...