A German internet user posted to YouTube the sound file of the 33-year-old right-wing extremist's speech on the last day of his trial last month.
He said he had received the recording from an elected member of the populist right Progress Party, of which Breivik was once a member.
In a bid to limit the spread of Breivik's extremist ideas, the Oslo district court had banned any broadcasting of images or sound from Breivik's 45-minute closing comments. It had however allowed his words to be published in the written press.
Mette Yvonne Larsen, one of the lawyers representing the victims' families, requested on Thursday that the sound file be removed from the public sphere.
"I have asked the Oslo court to check if any punishable acts have been committed," she told AFP.
"This shows on the one hand a lack of respect for a judicial decision ... and on the other hand it is a problem because this speech is a call to violence by a dangerous individual," she added.
A spokesperson at the Oslo court told AFP that the posting of the recording online was illegal and that the court was examining its options.
In his final speech on June 22nd, Breivik insisted his deadly attacks "were preventive ... in defence of my ethnic group," and were necessary to defend Norway against multiculturalism and a "Muslim invasion".
On July 22nd 2011, Breivik set off a car bomb outside government buildings in Oslo, killing eight people, before going to Utøya island, north-west of the capital where he shot and killed another 69 people, mostly teenagers.
The victims, the youngest of whom had just celebrated her 14th birthday, had been attending a summer camp hosted by the governing Labour Party's youth organization.
The verdict is expected on August 24th.