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.

In particular, she said the Islamist militant takeover of northern Mali had created a “safe haven” for terrorists to “extend their reach” and work with other extremists in North Africa, “as we tragically saw in Benghazi,” though she offered no clear evidence of such ties.

Now the Algerians say the plot to seize the gas complex in the desert was hatched in northern Mali as well. Indeed, Mokhtar Belmokhtar, the veteran militant who has claimed overall responsibility for the siege, is believed to be based there.

But the Algerian official did not say why the captured kidnapper’s assertion — that some fighters had taken part in both the Benghazi and Algerian attacks — should be considered trustworthy. Nor did he say whether it was obtained under duress.

Instead, he focused on the chaos unleashed by the recent uprisings throughout the region, leaving large ungoverned areas where extremists can flourish.

“This is the result of the Arab Spring,” said the official said, who spoke on condition of anonymity because investigations into the hostage crisis were still under way. “I hope the Americans are conscious of this.”

American counterterrorism and intelligence officials have said that some members of Ansar al-Shariah, the group that carried out the attack on the diplomatic mission in Benghazi, had connections to Al Qaeda in the Islamic Maghreb, one of the militant groups now holding northern Mali. But American officials have also said that the Qaeda affiliate played no role in directing or instigating that Benghazi attack.

Similarly, Egyptian security officials said they believed that a longtime Islamist militant from Egypt was involved in the gas field attack, but the officials did not know of any connection to the Benghazi attack as well.

Algeria was firmly opposed to the Western intervention to help topple Col. Muammar el-Qaddafi in Libya in 2011, and this nation’s conservative leadership viewed the Arab Spring with deep suspicion, making no secret of its desire to avoid any such occurrences.

Small-scale demonstrations here were quickly stifled, and ever since Algerian officials have not hesitated to point at what they see as the connection between popular demands for greater democracy that have swept the Arab world and the rise of Islamist militancy in the region.

Algerian officials says the militants who seized the gas field traveled through Niger and Libya, whose border is only some 30 miles from the plant at In Amenas. Mohamed-Lamine Bouchneb, the militant leading the attack at the site, had purchased arms for the assault in the Libyan capital, Tripoli, the senior official said.

The kidnappers had also gathered, undisturbed, at the southern Libyan town of Ghat, just across the border from Algeria, he said, depicting Libya as anarchic, without an effective military force and an ideal staging ground for attacks like the one launched a week ago.

Having already experienced a large-scale Islamist insurgency in the 1990s, in which perhaps as many as 100,000 were killed, Algeria had no intention of experiencing another, the official suggested. He defended the tough Algerian military assault during the standoff and dismissed criticism by foreign leaders that they were not informed of it in advance.

“We left it all up to the military chiefs,” he said. “Myself, I was only informed a half-hour afterwards.”

His assertion squares with the widely held view of Algerian analysts that the military, and in particular a cadre of elderly generals, holds a wide degree of autonomy in the country and often acts independently of civilian leadership.

The official said that Algeria could expect more terrorist attacks, despite having delivered sharp blows to militants over a period covering nearly 15 years.

“We’re waiting for more,” he said. “We are not out of the woods yet.”