The Department of Foreign Affairs says it is "pursuing all appropriate channels to seek further information" and is in close contact with Algerian authorities.
Spokeswoman Chrystiane Roy says Canada strongly condemns the "deplorable and cowardly attack."
There are reports that a news agency in Mauritania — Agence Nouakchott d’Information — has quoted an unnamed source with the militant group who says the hostage-takers included people from Mali, Egypt, Niger, Mauritania and Canada.
Meanwhile, a Canadian who was among the employees at the facility when the attack was launched on Wednesday is safe.
The bloody three-day standoff erupted when militants attempted to hijack two buses at the plant, were initially driven back and then seized the sprawling refinery, which is 1,300 kilometres south of Algiers.
They had claimed the attack came in retaliation for France's recent military intervention against Islamist rebels in neighbouring Mali, but security experts have said it must have taken weeks of planning to hit the remote site.
Since then, Algeria's government has kept a tight grip on information about a siege of the site.
The Algerian state news agency reported that 12 hostages had been killed since Thursday's start of an Algerian rescue operation at the Ain Amenas refinery, which is operated by energy company BP, Norwegian company Statoil and the Algerian state oil company, Sonatrach.
The agency also said that nearly 100 of the 132 foreign workers kidnapped by Islamic militants had been freed. It wasn't clear how the country's government arrived at the latest tally.
Algeria had long warned against military intervention against the rebels in northern Mali, fearing the violence could spill over its own long and porous border.
World leaders have expressed strong concerns in the past few days about how Algeria was handling the situation and its apparent reluctance to communicate.
— with files from The Associated Press.
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