“A number of other workers were taken hostage by the terrorists in separate locations, both at the residential compound and the gas facility.
“The precise numbers involved remain unclear at this stage but the hostages included British nationals, along with nationals of at least seven other countries and, of course, many Algerians.”
The terrorist attack began on Wednesday morning when heavily-armed militants launched a dawn raid, killing two people and injuring six others.
The militants – reportedly led by the veteran jihadist Mokhtar Belmokhtar – threatened previously to “eliminate” the hostages if they were attacked.
Mr Cameron said he has spoken to his Algerian counterpart Abdelmalek Sellal on four occasions since the siege began, including to offer experts in hostage negotiation and rescue.
He said: “From the outset I have been clear about our implacable opposition to terrorism and said that we will stand with the Algerians in their fight against these terrorist forces.
“But I also emphasised the paramount importance of securing the safety of the hostages.
“I offered UK technical and intelligence support - including from experts in hostage negotiation and rescue – to help find a successful resolution. And I urged that we and other countries affected should be consulted before any action was taken.”