At least 20 foreign hostages and some Americans escaped Thursday from an Al Qaeda-linked group who are now pinned down in an Algerian natural gas complex in the Sahara desert, according to Algerian and U.S. officials.

A senior U.S. official tells Fox News that at least one unarmed US drone is patrolling the Ain Amenas gas plant to provide intelligence on the situation. At least 20 gunmen attacked and took over the vast complex early Wednesday in retaliation for France's military intervention against Al Qaeda-linked rebels in neighboring Mali. Militants phoned Mauritanian media to say one of its affiliates had carried out the operation and that France should end its intervention in Mali to ensure the safety of the hostages.

Algerian Interior Minister Daho Ould Kabila said it appeared that the militants were hoping to negotiate their departure away from the area -- a notion he rejected.

"Security forces have surrounded the area and cornered the terrorists, who are in one wing of the complex's living quarters," Kabila said.

The militant group said Thursday that an strafing run executed by Algerian helicopters killed 35 hostages and 15 of their members, the Associated Press reports. But the claim could not be independently verified.

The group claiming responsibility -- called Katibat Moulathamine or the Masked Brigade -- told a Mauritanian news outlet that its leader, Al Qaeda strongman Moktar Belmoktar, was among the dead in the attack, which occurred when the kidnappers tried to leave the complex. They say seven hostages are still alive in Algeria, including Americans and citizens of the UK, Belgium and Japan.

A U.S. source tells Fox News that the attack did happen, but could not provide further details. Some of the Americans believed to have escaped have called home to their families, U.S. official sources say. An Algerian security official who spoke to the Associated Press on condition of anonymity said Americans were among the 20 hostages that escaped.

The militants, who initially claimed to have 41 hostages -- including seven Americans -- have been in a tense standoff since taking over the plant, which is located 800 miles south of the capital of Algiers. BP, which partly owns the plant, said in a statement on its website Thursday that the situation was still ongoing.

Some 30 Algerian workers fled the facility earlier Thursday, suggesting that the militants are having trouble managing the many hostages they have taken. Ireland's Foreign Ministry also said its hostage has been freed.

The France-based head of a catering company at the plant told French media before the latest escape that some 40 foreigners appeared to be held hostage in a separate area from the Algerian workers.

Regis Arnoux of the Marseille-based CIS Catering company said while electricity to the plant has been cut, it had at least three weeks of food supplies.

Algerian authorities, meanwhile, were talking with tribal Algerian Tuareg leaders in hopes of mediating the dispute.

Two people, one a Briton and the other Algerian, were killed in the militants' initial assault on the gas complex, which U.S. Defense Secretary Leon Panetta has called "a terrorist attack." The kidnapping is one of the largest ever attempted by a militant group in North Africa.

The hostage-takers are reportedly seeking a safe passage out of the isolated area, something Algerian authorities have already rejected.

Algerian Interior Minister Daho Ould Kabila also rejected theories that the militants had come from Libya, 60 miles away, or from Mali, more than 600 miles away. He said the roughly 20 well armed gunmen were from Algeria itself, operating under orders from Moktar Belmoktar, Al Qaeda's strongman in the Sahara.

Yves Bonnet, the former head of France's spy service, also dismissed the idea that the operation was specifically linked to the French action in Mali due to the amount of organization it involved.

"It was an operation conceived well in advance -- spectacular and needing a lot of preparation ... It was not at all an improvised operation," he told the Europe 1 radio. "The operation was probably already scheduled and simply getting all those people into the desert would take several days."

It is certainly the largest haul of hostages since 2003, when the radical group that later evolved into Al Qaeda in North Africa snatched 32 Western tourists. This is also the first time Americans have been involved.

BP, the Norwegian company Statoil and the Algerian state oil company Sonatrach, operate the gas field. A Japanese company, JGC Corp, provides services for the facility as well.

It was not immediately possible to confirm the identities of the hostages. Ireland said a 36-year-old Irish man was among them, and Britain and the U.S. said their citizens were taken, without giving numbers. The Norwegian company Statoil said 12 of its employees were captured -- nine Norwegians and three locals. Japanese media reported at least 3 Japanese among the hostages and the Malaysian government confirmed two of its citizens were taken.

British Foreign Secretary William Hague told BBC radio on Thursday that he has dispatched a team to Algeria to help at the British embassy there.

"Excuses being used by terrorists and murderers who are involved -- there is no excuse for such behavior, whatever excuse they may claim," he said. "It is absolutely unacceptable, of course. It is, in this case, the cold-blooded murder of people going about their business. So there is no excuse, whether it be connected to Libya, Mali or anywhere else."

In Rome on Wednesday, U.S. Defense Secretary Leon Panetta declared that the U.S. "will take all necessary and proper steps" to deal with the attack in Algeria. He would not detail what such steps might be but condemned the action as "terrorist attack."

BP said it would not identify staff members who were taken hostage for security reasons.

"BP's overriding priority is to do all we can to ensure the safety of our staff and to support their families during this anguishing time," BP CEO Bob Dudley said in a statement. "All our efforts are focused on supporting the authorities to secure a peaceful resolution of the situation and the safe return of our colleagues and all other workers being detained."

The Associated Press contributed to this report.