Belmoktar, the man behind the group claiming responsibility for the attack and kidnappings, is known for seizing hostages.
French counterterrorism forces have long targeted Belmoktar, an Algerian who lost an eye fighting in Afghanistan in his teens. Libyan sources said he spent several months in Libya in 2011, exploring cooperation with local jihadist groups and securing weapons.
The militants said they carried out the operation because Algeria allowed French forces to use its airspace in attacking Islamist militants in Mali. Media in the region reported the attackers issued a statement demanding an end to "brutal aggression on our people in Mali" and cited "blatant intervention of the French crusader forces in Mali."
French Prime Minister Jean-Marc Ayrault said the Algerian hostage situation "confirms the gravity of the terrorist threat and the necessity to fight it with a determined and united front."
That sentiment was echoed by Clinton, the top U.S. diplomat. She stressed the need for a concerted, international effort to address terrorist and other threats around Africa.
"It is absolutely essential that, while we work to resolve this particular terrible situation, we continue to broaden and deepen our counterterrorism cooperation," she said Friday. "It is not only cooperation with Algeria, it is international cooperation against a common threat."