In his statement, he admits to drug use and apologises to his family.
According to Se og Hør , Marius spent more than 30 hours in police custody on Sunday 4 August following an "incident in an apartment" in Frogner, Oslo.
The woman diagnosed with a concussion after being admitted to hospital.
Marius, who is the stepson of Crown Prince Haakon , has spoken out via his lawyer, Oyvind Braitlin, in a statement shared with Norwegian outlet NRK.
He said: "Last weekend something happened that should never have happened. I committed bodily harm and destroyed objects in an apartment in the intoxication of alcohol and cocaine after an argument.
"I have several mental disorders which mean that throughout my upbringing and adult life, I have had, and still have, challenges. I have struggled with substance abuse for a long time, something I have been in treatment for in the past. I will now resume this treatment and take it very seriously.
Marius continued: "The drug use and my diagnoses do not excuse what happened in the apartment at Frogner on the night of Sunday last weekend. I want to be responsible for what I have done, and will explain myself truthfully to the police.
"For me, the most important thing is to say sorry to my girlfriend. She deserved neither what happened that night, nor the extreme pressure from both the Norwegian and foreign press afterwards. Being pursued by photographers and journalists at a time like this I know has been tough to stand in."
He ended his statement by saying: "I also want to apologise to my family. I know that my actions have greatly affected you. So to you my love, I'm sorry. This should never have happened and I take full responsibility for my actions."
Speaking about his client to Norwegian channel TV2, Marius' lawyer Mr Bratlien said: "He has not formally taken a position on guilt as he has not been questioned, but in reality this is an admission of guilt after the charge."
Crown Princess Mette-Marit, 50, postponed her attendance at the Paris 2024 Olympics , to be with her son at her official residence, Skaugum, in Asker, just outside of Oslo. She later joined her husband, Crown Prince Haakon, at the athletics and handball events.
Before his wife joined him in Paris, Haakon called the incident a "serious matter" in a brief comment to the media, before adding: "In our family, as in all families, it is sometimes important to be there. This time it was me who went while she stayed at home."
Marius is the firstborn son of Crown Princess Mette-Marit from her relationship with convicted felon Morten Borg. He was raised by his mother and stepfather, Haakon, following their marriage in 2001.
Marius does not have a public role and is not in the line of succession to the Norwegian throne.
Mette-Marit and Haakon share two children – Princess Ingrid Alexandra, 20, and Prince Sverre Magnus, 18.
The Norwegian royals are preparing for the forthcoming wedding of Haakon's sister, Princess Martha Louise , to American shaman Durek Verrett on 31 August.
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