Mr. Sarkozy said, “This crime committed against Michel Germaneau will not go unpunished.”

A retired engineer, Mr. Germaneau had been working for a humanitarian association when he was abducted in late April. His captors demanded freedom for Qaeda prisoners in France and elsewhere in exchange for his release. On July 11, the group threatened to kill him if its conditions were not met within 15 days.

Image President Nicolas Sarkozy of France spoke at the Elysee Palace in Paris on Monday. Credit... Philippe Wojazer/Reuters

French officials, however, said the group had never offered more than vague demands and refused all efforts to negotiate.

Mr. Germaneau’s death was “not preceded by the slightest beginnings of a dialogue with French or local authorities,” Mr. Sarkozy said. Al Qaeda’s ultimatum, he said, was “in fact no more than the announcement of a scheduled killing.”

On Sunday, Al Jazeera broadcast an audio recording attributed to Al Qaeda in the Islamic Maghreb that announced Mr. Germaneau’s death. The French Defense Ministry said it authenticated the recording on Monday.

“Sarkozy was unable to free his compatriot through this failed operation, but he definitely opened one of the gates of hell on himself, his people and his nation,” said a man identified in the audio as Abu Musab Abdel-Wadoud, a leader of the abductors.