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 Somalia, Yemen and Pakistan.

Until now, the U.S. has focused on feeding intelligence to allies about Mr. Belmokhtar and his terrorist group, which is an offshoot of al Qaeda's North African affiliate. That strategy has helped the U.S. maintain an arm's-length approach to counterterrorism operations in northwest Africa, where Islamist militants have carved out a haven.

The push by U.S. military and intelligence officials to list Mr. Belmokhtar as a target comes as the militants face a potential guerrilla war with French and African military forces in northern Mali, a base of operations for the Algerian.

U.S. officials said that Mr. Belmokhtar, whose group has armed itself in part with Libyan weapons, stands as a key example of the dangers of unchecked terrorist aspirations and capabilities in the wake of the Arab Spring, which saw several iron-fisted dictatorships give way to more-chaotic elected governments.