WASHINGTON—The Central Intelligence Agency's drone program has come under attack by human-rights groups who say they are preparing a broad-based campaign that will include legal challenges in courts in Pakistan, Europe and the U.S.

The nascent effort is being modeled after the challenges brought by some of the same groups against the administration of President George W. Bush over detentions at the Guantanamo Bay military prison and in secret CIA "black sites," say lawyers involved in the planning.

The...