WASHINGTON—Senior U.S. officials are pressing to mark for the killing or capture of the self-proclaimed mastermind of last month's attack on an Algerian natural-gas facility that claimed the lives of 37 foreign hostages, including three Americans.

Adding the Algerian militant Mokhtar Belmokhtar to a U.S. targeted-killing list would represent a significant U.S. expansion into northwestern Africa, extending the reach of the U.S. program of drone strikes and other lethal counterterrorism operations, which have concentrated on...