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Mr. Cameron declined to second-guess Algerian tactics at what he called “one of the most remote places on Earth.”

The sprawling complex is Algeria’s third-largest natural gas facility and is near the desert town of Ain Amenas on Algeria’s border with Libya.

“The responsibility for these deaths lies squarely with the terrorists who launched a vicious and cowardly attack,” Mr. Cameron said.

Japanese officials were the most critical of the Algerian military assaults.

“We never tolerate terrorism,” Japan’s Chief Cabinet Secretary Yoshihide Suga told reporters Sunday in Tokyo.

“But we had asked the Algerian government to put top priority on the lives [of the hostages]. It’s extremely regrettable to see developments like this.”

This article is based in part on wire service reports.