ALGIERS — Several Egyptian members of the squad of militants that lay bloody siege to an Algerian gas complex last week also took part in the deadly attack on the United States Mission in Libya in September, a senior Algerian official said Tuesday.

The Egyptians involved in both attacks were killed by Algerian forces during the four-day ordeal that ended in the deaths of at least 38 hostages and 29 kidnappers, the official said. But three of the militants were captured alive, and one of them described the Egyptians’ role in both assaults under interrogation by the Algerian security services, the official said.

If confirmed, the link between two of the most brazen assaults in recent memory would reinforce the transborder character of the jihadist groups now striking across the Sahara. American officials have long warned that the region’s volatile mix of porous borders, turbulent states, weapons and ranks of fighters with similar ideologies creates a dangerous landscape in which extremists are trying to collaborate across vast distances.

Secretary of State Hillary Rodham Clinton, who is scheduled to testify before Congress on Wednesday about the Libyan attack that killed the American ambassador and three staff members, raised the specter of regional cooperation among extremists soon after the mission in Benghazi was overrun.