Among the hostages are American, British, French, Japanese and Norwegian citizens, and the Algerian state-run APS news agency reported that a British national was one of the two people who were killed.
The Mauritanian News Agency ANI reported that an alleged spokesman for the militants claimed as many as 40 foreigners had been taken.
Militants linked to the terrorist network al-Qaeda have claimed responsibility for the attack and said that it was in retaliation for the French military operations in neighboring Mali, where an Islamist insurgency has broken out.
BBC reported that the group, the Khaled Abu al-Abbas Brigade, is apparently headed by a man named Mokhtar Belmokhtar, a former senior commander of al-Qaeda in the Islamic Maghreb (AQIM).
"We are holding the Algerian and French governments, and the hostages' countries, entirely responsible for their slowness in satisfying our demands, foremost of which is an immediate halt to the aggression against our brothers in Mali," a spokesman for the Brigade stated.
Reportedly, Algerian employees at the gas plant were released by the militants.
Norway's Prime Minister Jens Stoltenberg expressed concern for the 13 Norwegian employees believed to be held hostage at the gas facility.
"We've asked the Algerian authorities to put the life and health of the hostages above all," Foreign Minister Espen Barth Eide said during a news conference.
Ireland's Foreign Minister Eamon Gilmore said one Irish citizen had been kidnapped, and that Dublin is "ready to use all the resources available to us to ensure that our citizen is released as soon as possible."
The Algerian state oil company Sonatrach operates the In Amenas gas field along with British oil giant BP and the Norway-based Statoil company. The facility is located 800 miles southeast of the capital city of Algiers, near the Libyan border.