Algeria's state news agency APS says that the military operation to free hostages at a remote desert gas facility has ended.
The news agency quotes an unnamed official source on Thursday as announcing the end of the government operation but gives no further details.
Militants claim 35 hostages and 15 kidnappers were killed in Thursday's military raid. Algerian Information Minister Mohammed Said has confirmed there were fatalities but didn't provide a number.
Algerian media reports say several foreigners were rescued.
The military operation comes after militants took tens of foreigners and Algerians hostage on Wednesday at the In Amenas installation, 800 miles south of Algiers, in the Sahara Desert.
The hostage-takers were demanding that France cease its operation against militants in Mali.
The United States says it is concerned about reports of loss of life in the crisis.
White House spokesman Jay Carney said he could not confirm the number of casualties or their identities.
"Right now our priority is determining the status of the Americans involved and gaining a full understanding of what took place," Carney said. "This is a fluid situation. We are seeking clarity from the Algerian government about this matter."
A spokesman for British Prime Minister David Cameron said Britain was not given prior notice of the Algerian hostage rescue operation.
French President Francois Hollande said the Algerian hostage crisis shows the French intervention in neighboring Mali was justified.
Algerian Interior Minister Daho Ould Kablia said the kidnappers were led by Mokhtar Belmokhtar, a veteran Islamist guerrilla who fought in Afghanistan and set up his own group in the Sahara after falling out with other local Al-Qaeda leaders.
Belmokhtar's links to those who seized towns across northern Mali last year are unclear.
Based on reporting by AFP, dpa, Reuters