"PST has received information that a Norwegian citizen of Somali origin may have been involved in the planning and execution of the attack," the agency said in a statement on Thursday. "PST has decided on this basis to initiate an investigation."
The agency said it had sent officers to Nairobi, where they would work with Kenyan police.
"The enquiry will primarily be aimed at helping prevent new terrorist acts and [determining] to what degree the Norwegian... was involved in the attack," it said.
The Star, a Kenyan newspaper, has reported that Kenyan police now believe that the attack was at least partly planned in Norway.
According to the newspaper, police investigating the attacks have written to the Norwegian Embassy requesting assistance locating a Somali refugee still living in Norway.
"He is well known in Daadab [a refugee camp in the north of Kenya]. We think part of the planning was done in the camp," a police source told the newspaper.
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The Somali insurgent group al-Shabaab has claimed responsibility for the terrorist attack, which left at least 67 people dead.
According to VG newspaper, the Norwegian Somali Kenyan police have requested help locating is not Ikrima al-Muhajir, another Somali who has spent time living in Norway, who was the target of a US raid against Somalia last week.