The Obama administration is condemning the attack. Defense Secretary Leon Panetta called the incident a "terrorist attack."
Sandwiched between Mali and Libya in the north, Algeria is Africa's biggest country and has been an ally of the U.S. and France for years in fighting terrorism.
The militant group Katibat Moulathamine, or the Masked Brigade, said the attack was revenge for Algeria's support of France's operation against al Qaeda-linked Malian rebel groups. The Algerian government allowed French fighter jets into its air space as French troops try to regain control of the capital from Islamic extremists, with its mission dubbed Operation Serval.
The group said it was holding 41 foreigners, including seven Americans. It is believed a number of British, Japanese and French nationals are also being held hostage. In a briefing, state department spokesperson Victoria Nuland confirmed that U.S. citizens are among the hostages.
"In order to protect their safety, I'm not going to get into numbers, I'm not going to get into names, I'm not going to get into any further details as we continue to work on this situation with Algerian authorities and also their employers," Nuland said.
The natural gas field is jointly operated by BP and a Norwegian company. Algerian forces have surrounded the complex.
"Algeria will not respond to terrorist demands and rejects all negotiations," announced Algeria's top security official, Interior Minister Daho Ould Kablia on television.
At least one foreign intelligence agency says the attack was too well orchestrated to have been planned in such a short period of time. Operation Serval was just launched on Jan. 11.
In addition to those killed - one of them a Briton - six were wounded in the attack, including two foreigners, two police officers and two security agents, the state news agency reported.
ABC News and The Associated Press contributed to this report.