"We have received a complaint from the family of a victim that is faulting the police for the way in which it carried out its duties on Utøya on July 22nd 2011," a spokesman for the Norwegian Bureau for the Investigation of Police Affairs, Paal Henrich Berle, told AFP.
The complaint refers "more specifically to whether the police could have arrived at the scene sooner and, in such case, saved lives," he said.
On July 22nd 2011, Breivik set off a car bomb outside the government offices in Oslo, killing eight people, before going to Utøya, north-west of the capital, where he spent more than an hour gunning down another 69 people, mostly teenagers, attending a Labour Party youth camp.
Earlier this month, an independent commission presented a scathing report on the authorities' handling of the attacks, concluding that Breivik could have been arrested on Utøya sooner if police hadn't bungled their response.
The only police helicopter was out of action because its crew were on holidays, and a SWAT team took more than an hour to finally make it to the island, forced to use a pleasure boat after their inflatable almost sank.
Norway's national police commissioner resigned days after the report was presented.
Berle said the Bureau had not yet decided whether to open an inquiry into the police response.
Prime Minister Jens Stoltenberg, heavily criticized in the report for Norway's lack of preparedness, appeared before an extraordinary session of parliament on Tuesday to apologize for the authorities' shortcomings.
Breivik, a 33-year-old right-wing extremist, was last week found sane by an Oslo court and sentenced to Norway's maximum sentence of 21 years, which can be extended indefinitely if he is still considered a threat to society.