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In a 33-page-long letter, sent to AFP and seen by Reuters, Breivik said he was committed to bring about change by peaceful means and wanted to set up a party called the Norwegian Fascist Party and the Nordic League.
"My heart bleeds as an ex-militant for the barbarity I perpetrated on July 22," the 35-year-old wrote, referring to the day when he planted a car bomb in central Oslo killing eight people and gunned down 69 more on Utoeya Island.
"As an ex-militant, the most important thing in my life now is to make sure that something like this never happens again. The whole purpose with the NFP and the NL is to ensure that it never happens again."
During his trial in 2012, Breivik showed no compassion for his victims, saying in court that he would do it all over again if he had the chance.
He said he could apologise - but only under certain conditions.
"I am willing to apologise for my actions ... the day the 'Gerhardsen/Hauge doctrine' of permanent political exclusion for democratic fascists ceases," writes Breivik, referring to Einar Gerhardsen and Jens Christian Hauge, two Labour ministers who dominated Norway's social democratic, post-war politics.
He sent the letter, written in Norwegian and signed "Anders Behring Breivik, party secretary and parliamentary candidate for the NFP & NL", from his prison in Skien in southern Norway where he is serving the maximum time in prison of 21 years. He will not be released if he is deemed a threat to society.
Breivik said he had been denied the right to set up a party by prison authorities, who he said confiscate letters he sends to seek signatures needed to set up a party. In Norway prisoners keep their rights as citizens, such as the right to vote.
In the letter, Breivik said he would consider filing a lawsuit if the Norwegian justice ministry did not remove barriers to him setting up a party within 30 days.
Officials at Skien prison were unavailable to comment.