(CNN) -- Two days after Islamist militants abducted an undetermined number of hostages -- including Westerners -- at a gas plant in a remote section of Algeria, "ongoing activity at various locations" was continuing, a British official said Friday.
It was not clear whether that activity represented "mopping up and checking" or "something more active" being carried out by Algerian forces against the abductors, the official told CNN.
Algerian forces launched their operation upon noticing the hostages being moved toward "a neighboring country," where kidnappers could use them "as a means of blackmail with criminal intent," Algerian Communications Minister Mohamed Said told state television on Thursday.
The British official said there was a "significant" number of British victims and others were unaccounted for.
British Foreign Secretary William Hague was to release more information Friday from Australia, and a parliamentary statement will be issued, the official said.
The official's account was in line with Prime Minister David Cameron's warning of "bad news ahead" issued late Thursday
Algerian troops fired on at least two SUVs trying to leave the kidnapping site, Algerian radio said, citing local sources. And an Algerian reporter saw clashes near the site, the Algerian Press Service and radio reports said.
"There were a number of dead and injured, we don't have a final figure," Said reported.
Earlier, Algeria's state media reported that all Algerian nationals who had been held hostage were free: some had fled, while others were released. The hostages still detained are foreigners, Algerian Interior Minister Dahou Ould Kablia said.
In addition to the hundreds of freed workers, 30 Algerian workers escaped and were picked up by helicopters, the APS report said.
Nearly 600 workers and four foreign nationals -- two Scots, a Kenyan and a French citizen -- were free by late Thursday after the Algerian military operation, the state-run Algerian Press Service reported.
But some hostages were still presumably being held. "It is a fluid situation, it is ongoing," Cameron told the Reuters news agency. "I think we should be prepared for the possibility of further bad news, very difficult news, in this extremely difficult situation."
The Algerian military operation led to numerous casualties and was over by Thursday evening, the Algerian Press Service said.
But U.S. and British officials predicted it would resume Friday during the day.
"There are still hostages, and there are still terrorists," a senior U.S. official said. "So tomorrow is another day."
Two people -- an Algerian and British national -- died Wednesday when the Islamist militants attacked, the same news agency said.
The Algerians and foreign workers were taken hostage early Wednesday in an assault carried out apparently in response to France's offensive in neighboring Mali. The gas field is 60 kilometers (40 miles) west of the Libyan border and 1,300 kilometers (about 800 miles) from the Algerian capital, Algiers.
The kidnappers were equipped with AK-47 rifles and put explosives-laden vests on some of the hostages, a U.S. State Department official said.
On Wednesday, the attackers had put the number of hostages at "more than 40," including seven Americans, two French, two British and other Europeans. Another Islamist group told the Mauritanian News Agency there were 41 "Westerners."
The APS, though, reported that slightly more than 20 foreign nationals were being held.
Officials from Norway, the United States, Japan and Britain said some of their nationals were among the hostages.
Three workers for a Japanese engineering company that was working on the site had been contacted and were safe, said Takeshi Endo, a senior manager for JGC Corp. But the company had not been able to contact 14 others, he said.
"There is so much conflicting information on safety of the hostages," Chief Cabinet Secretary Yoshihide Suga told reporters in Tokyo. "Safety of 14 Japanese citizens still remains unknown."
He said Japanese officials had urged the Algerian government to avoid exposing the hostages to danger. "We are terribly disappointed about the Algerian's military operation," he said.
Nine Norwegian employees of Statoil were unaccounted for, while five Norwegian nationals -- as well as three Algerians -- who work for the company were safe, the company said in a statement.
CNN affiliate BFM-TV reported that a French nurse who was working on the site at the time of the attack was freed.
Former hostage Stephen McFaul had plastic explosives strapped around his neck, duct tape over his mouth and rope around his hands, his brother Brian McFaul told CNN from Belfast.
McFaul made a break for freedom after the vehicle he was in -- one of several targeted by Algerian fighters -- crashed, with the explosives still around his neck.
"The joy was unreal," Brian McFaul said upon hearing his brother was safe. "I haven't seen my mother move as fast in all my life, and my mother smile as much, hugging each other ... You couldn't describe the feeling."
Americans were among the hostages at the In Amenas facility in Algeria, White House spokesman Jay Carney said without specifying how many. There could be as few as three American hostages, two U.S. officials said Wednesday.
One of the kidnapped Americans is a Texas man, a family member told CNN.
By Thursday night, some Americans had been freed and had spoken with relatives back home, while others remained unaccounted for, U.S. officials said.
"This incident will be resolved -- we hope -- with a minimum loss of life," said U.S. Secretary of State Hillary Clinton. "But when you deal with these relentless terrorists, life is not in any way precious to them."
The man behind the group claiming responsibility for the attack and kidnappings is a veteran jihadist known for seizing hostages.
Moktar Belmoktar, an Algerian who lost an eye fighting in Afghanistan in his teens, has long been a target of French counterterrorism forces. Libyan sources said he spent several months in Libya in 2011, exploring cooperation with local jihadist groups and securing weapons.
Two oil companies that operated at the site -- BP and Statoil -- said they were pulling non-essential personnel from Algeria.
"Our focus is 100 percent on the safety and welfare of those people and their families, and we are now beginning a staged and planned reduction in non-essential workforce on a temporary basis, pulling them out of the country," said BP Vice President Peter Maher from London.
The militants said they carried out the operation because Algeria allowed French forces to use its air space in attacking Islamist militants in Mali. Media in the region reported that the attackers issued a statement demanding an end to "brutal aggression on our people in Mali" and cited "blatant intervention of the French crusader forces in Mali."
U.S. Defense Secretary Leon Panetta, in Europe meeting with NATO allies, called the hostage-taking "a terrorist act."
Japan and the United Kingdom sent officials to Algeria. French President Francois Hollande earlier confirmed the presence of French citizens on the site but would not say whether any were hostages.
Cameron -- who canceled a planned Friday speech in the Netherlands -- talked Thursday with U.S. President Barack Obama about the situation, according to a Downing Street statement.
Before Algeria launched its military operation, U.S. officials had urged the Algerians to be cautious and make the hostages' safety their first priority, an Obama administration official said.
Algerian government officials did not warn their U.S. counterparts about the raid, the official said.
A senior U.S. official said U.S. officials did not trust the information they were getting from the Algerians, "because we hear one thing and then we hear something else."
Though there was concern that the Algerians' tactics may have put hostages in jeopardy, the official acknowledged they could have hit even harder.
"In all fairness, they could have ended it today," the senior U.S. official said. "They haven't used all the severeness they could. They know hostages are left."
CNN's Tom Watkins, Joe Sterling and Greg Botelho wrote this story from Atlanta. CNN's Dan Rivers, Elise Labott, David Mattingly, Athena Jones, Barbara Starr, Jethro Mullen, Tim Lister and Faith Karimi contributed to this report, as did journalists Peter Taggert from Belfast and Said Ben Ali from Algiers.