over the haste of an Algerian military assault on the remote desert site, the APS news agency said special forces had freed more than 670 hostages, among them 573 Algerians and around 100 foreigners.
The army was still trying to free those foreigners still held by al Qaeda-linked militants across the complex deep in the Sahara near the Libyan border, APS said.
It "is trying to reach a peaceful solution before neutralising the terrorist group that is holed up in the plant and freeing a group of hostages still being held there."
British Prime Minister David Cameron warned that the In Amenas plant was a "large and complex site and they are still pursuing terrorists and possibly some of the hostages in other areas of the site."
Some of those who escaped or spoke of their ordeals said they had had explosives wrapped around their necks. Others said they hid, petrified, under beds, in gaps above ceilings or wherever they could.
The Algerian operation was launched on Thursday, a day after kidnappers seized the plant to avenge what they said was Algiers' support for French air strikes in neighbouring Mali.
The kidnappers said 34 captives were killed in the army assault, but an Algerian security source called that "fantasy," saying 18 of more than 30 Islamist gunmen were killed.
Cameron, who said he was "disappointed" not to have been told by the Algerians in advance, said "significantly" fewer than 30 British citizens remained at risk at the field, operated jointly by Britain's BP, Norway's Statoil and Sonatrach of Algeria.
BP said a "small number" of its staff were unaccounted for on Friday, adding that it had evacuated hundreds of workers from the complex and other fields.
US Defence Secretary Leon Panetta said in London US officials were "working around the clock" to secure the safe return of an unknown number of American hostages.
"Terrorists should be on notice that they will find no sanctuary, no refuge. Not in Algeria, not in north Africa, not anywhere," he said.
A senior US official said Washington "strongly encouraged" the Algerian authorities to make the hostages' safety their top priority.
Japanese plant builder JGC said it had now accounted for 17 of its employees, but that the whereabouts of 61 more remained unknown.
Statoil said another of its Norwegian employees was now safe, but that the fate of eight others was unknown.
France said two of its nationals had returned safely but it had no word on two others reportedly seized. Vienna said one Austrian had been released.
One man from Northern Ireland, Stephen McFaul, escaped. His brother said he fled when the convoy he was in came under army fire. He had earlier "had explosives tied around his neck."
Alexandre Berceaux, who works for France's CSI Catering, said he stayed in his room and hid before finally being freed by Algerian troops on Thursday evening.
"I was under the bed and I put boards everywhere just in case," Berceaux said. "I had a bit of food, a bit to drink. I didn't know how long it would last."
The gunmen from a group known as "Signatories in Blood" want to negotiate an end to French intervention in Mali and exchange American hostages for prisoners held in the United States, Mauritanian news agency ANI quoted sources close to their leader, Mokhtar Belmokhtar, as saying on Friday.
ANI reported that Belmokhtar, a veteran Algerian Islamist with Al-Qaeda ties who has claimed responsibility for Wednesday's attack, had proposed that Paris and Algiers negotiate "an end to the war being waged by France in Azawad" (northern Mali).
In what ANI said was a video that would be released to media, he also proposes exchanging American hostages held by his group for Egyptian Omar Abdul Rahman and Pakistani Aafiah Siddiqui, jailed in the United States on charges of terrorist links.
Algeria has insisted it will not negotiate with "terrorists."
Earlier, a spokesman for the group said that, "taking into account the suffering of the Algerian people, we promise the regime in place that there will be more operations," ANI said.
The hostage drama dragged Algiers and Western powers into the Mali conflict, taking the spotlight off French and government troops battling Islamists who control the country's vast desert north.
The Malian army has retaken the centre of Konna, which had fallen to Islamists advancing from the north and sparked French military intervention, the military and a regional security source said on Friday.
On Thursday, more French troops poured into Mali, boosting their number to 1,400, Paris said. At full strength the force will reach 2,500 soldiers.
French Foreign Minister Laurent Fabius said he would attend an emergency summit of west African states on Saturday to help accelerate the deployment of a regional military force.