PST chief Marie Benedicte Bjørnland — who is known to be a plain speaker on such matters — was addressing a security conference in the Swedish ski resort town of Sälen, where the New Years' Eve assaults in Cologne were discussed.
German authorities are investigating around 500 complaints over sex attacks that took place in Cologne on New Year's Eve — involving men of Arab or North African appearance.
In Norway, police are working with their Swedish colleagues as they investigate allegations about a string of sexual attacks carried out by Afghan refugees at a Stockholm music festival, which some say have been covered up by the authorities.
"A strong increase in immigration, particularly from Muslim countries, can cause other long-term challenges. When a large number of asylum seekers come to a local community, it can have unfortunate consequences," Bjørnland told delegates.
"One cannot take for granted that new population groups will automatically adapt the norms and rules of the Norwegian society," she added.
Bjørnland went on to tell broadcaster TV2 that accepting large numbers of foreigners can lead to violent clashes and the growth of far-right extremist groups.
"If in the long term, you see a growth of parallel societies, radicalization and extremist environments, then we will have challenges as a security agency," she said.
Norway runs courses for male refugees about Norwegian sexual norms and laws, to help them adapt to a country where women have greater freedoms, wear fewer clothes and walk alone in public. The course explains that some sexual practices deemed 'honorable' in some Middle East and North African countries are not acceptable in the West. The course manual states:
"To force someone into sex is not permitted in Norway, even when you are married to that person."
Norway has also kept strict control over migrants reaching its borders, deporting 7825 people out of the country in 2015, an all-time record.