Islamist terrorists stormed the facility Wednesday. BP is a consortium member alongside state-owned Sonatrach and Norwegian major Statoil.
"BP confirms that the major security incident at the In Amenas joint venture site in Algeria is continuing. The situation on site remains unresolved and fragile," the company said in a statement. "Armed groups still occupy the site and hold a number of site personnel."
Radical groups said the incident was in response to multilateral military operations in neighboring Mali. The facility is located, however, near the country's eastern border with Libya.
Some on site personnel have been killed during the crisis. British Foreign Secretary William Hague said there's no excuse for attacks on civilian employees.
"It is in this case the cold blooded murder of people going about their business," he said in a statement. "So there is no excuse whether it be connected to Libya, Mali or anywhere else."
Statoil, for its part, said five of its 17 employees at or near the facility are safe. The remaining 12 are confirmed as hostages. A number of Westerners are among those held captive, though their respective governments have kept details close to their chests out of concern for their safety.
Algerian state media reports Thursday that 30 nationals were able to escape from their captors.
The government there said the kidnappers were Algerian nationals who were following orders from al-Qaida in the Islamic Maghreb leader Mokhtar Belmokhtar. The kidnappers say they have as many as 41 hostages, the BBC reports.