A high-level Algerian government official said 20 Islamic militants in three unmarked vehicles attacked the facility and took as many as 30 hostages, though he said there were "no precise figures for now," The New York Times reported. Unidentified oil industry officials said there may be as many as 40 hostages.
Algeria's state-run news agency reported at least two people were killed, including one British national. The hostages included American, British, French, Norwegian and Japanese citizens, the Times said.
Security forces had "encircled the base" so "no one can leave," the unidentified official told the Times.
The Times said news agencies in Algeria and Mauritania reported al-Qaida in the Islamic Maghreb claimed responsibility for the attack.
"The Algerian authorities will not respond to the demands of the terrorists and will not negotiate," the state-run news agency quoted Algerian Interior Minister Daho Ould Kablia as saying.
State Department spokeswoman Victoria Nuland declined to specify at a briefing how many Americans were taken.
"The best information that we have at this time is that U.S. citizens are among the hostages," she said. "I hope you will understand that, in order to protect their safety, I'm not going to get into numbers, I'm not going to get into names."
U.S. Defense Secretary Leon Panetta, traveling in Italy, said the United States would react appropriately to the situation, the Times said.
"By all indications this is a terrorist act," Panetta said. "It is a very serious matter when Americans are taken hostage along with others. I want to assure the American people that the United States will take all necessary and proper steps that are required to deal with this situation."
Guards repelled the initial early morning attack by terrorists, the Interior Ministry said. The terrorists then laid siege to part of the site and "captured an undetermined number of workers, including foreigners," it said.
The attack appears to be a response to French military strikes on al-Qaida forces battling government forces trying to regain control of northern regions of Mali held by the militant group, the British newspaper The Daily Telegraph reported.
British oil giant BP said the incident occurred at an installation in Amenas. BP runs the facility in partnership with Norwegian and Algerian interests.