(CNN) -

One American worker is among the 12 who have been killed during a hostage standoff at a natural gas complex in Algeria, U.S. officials and Algerian state news said Friday.

The Associated Press reported that officials identified the dead American as Frederick Buttaccio, a Texas resident. However, it was unclear how he died. The officials told the wire service that they recovered Buttaccio's remains on Friday and notified his family. Officials spoke to the AP on condition of anonymity because they weren't authorized to speak publicly on the matter.

The AP reported that the Obama administration was seeking to secure the release of other Americans still being held by the militants.

Meanwhile, CNN reported that at least two Americans also had escaped.

After days of chaos, drama and an untold number of deaths, Algerian special forces troops are holding their fire -- and hoping for a peaceful resolution -- to the hostage crisis at a gas facility in the North African nation's remote eastern desert.

Survivors have described their harrowing escapes from Islamic militants who attacked Wednesday. Some invented disguises, others sneaked out with locals, and at least one ran for his life with plastic explosives strapped around his neck.

Yet others didn't make it -- either because they were killed or are still being held.

Algerian troops earlier this week staged a military offensive that some nations slammed, claiming it didn't make hostages' safety the top priority. For now, they are trying a different tact, the state-run Algerian Press Service reported Friday evening.

"The special forces ... are still seeking a peaceful settlement before neutralizing the terrorist group currently entrenched in the refinery, and free a group of hostages who are still detained," according to the official report.

It isn't clear how many hostages were seized by the Islamic militants and how many were initially or are still being held. The Thursday military operation ended with 650 hostages -- including 100 foreigners -- freed, while at least 12 were killed, reports the Algerian Press Service. The dead include one American, according to U.S. officials, as well as one French and one British citizen.

At least 30 foreign workers were unaccounted for, according to the official media report, which has not been separately confirmed.

British Prime Minister David Cameron said Friday that "significantly" fewer than 30 of his countrymen were still hostages. There could be as few as three Americans still being held, two U.S. officials said earlier this week.

The fate of eight workers with Norway's Statoil, some of them Norwegians, is unclear, according to the company. The same is true for 14 Japanese, Chief Cabinet Secretary Yoshihide Suga told reporters in Tokyo. And Malaysia's state-run news agency, citing its foreign ministry, reported Thursday two of its citizens were held captive.

A spokesman for Moktar Belmoktar, a veteran jihadist who leads the Brigade of the Masked Ones -- a militant group associated with al Qaeda in the Islamic Maghreb -- reportedly offered to free U.S. hostages in exchange for two prisoners.

The prisoners are Sheikh Omar Abdel Rahman, who orchestrated the 1993 World Trade Center bombing, and Aafia Siddiqui, a Pakistani woman jailed in the United States on terrorism charges, the spokesman said in an interview with a private Mauritanian news agency.

Asked Friday about the offer, State Department spokeswoman Victoria Nuland rejected it, restating U.S. policy of not negotiating with terrorists.

With the situation remains very much unsettled, officials from countries involved in the crisis said they have no doubt who is to blame.

"This is an act of terror," U.S. Secretary of State Hillary Clinton said Friday. "The terrorists ... are the ones who have assaulted this facility (and took) hostage Algerians and others (from) around the world who were going about their daily business."

A dangerous escape

The ordeal began when the militants -- apparently angry about Algeria's support in a rout of their comrades in neighboring Mali -- targeted the gas field, which is operated by Algeria's state oil company in partnership with foreign companies.

At the start of the siege, the militants gathered all Westerners into one group and tied them up, according to survivors.

The kidnappers were equipped with AK-47 rifles and put explosives-laden vests on some hostages, a U.S. State Department official said.

Some escaped by disguising themselves, according to Regis Arnoux, who runs a catering firm at the site and spoke to some of his 150 employees who were freed. He said they all were "traumatized."

Some Algerian hostages were free to walk around the site but not leave, according to Arnoux. A number of them still escaped.

As the Algerian military launched its operation Thursday, the militants moved some hostages, according to one survivor's account.