"So I was given every opportunity to leave of my own will but, as any parent would understand, you don't leave your children behind.
"So I effectively wasn't able to leave either."
Ms Puriri left the apartment on February 23, but her children remain with Mr Azzaoui.
She commended the efforts of New Zealand consul Barbara Welton who arrived at the home with about 10 gendarmes bodyguards to resolve the situation.
"She was instructed not to leave the house without the New Zealand citizens. She did sit down on the floor and refuse to leave.
"I really admire her doing that because there were in excess of 50 people, some of them armed police and gendarmes in the house, and she just stood her ground as she was supposed to do. I'm really grateful for her support.
Ms Puriri said the stand-off lasted about "six or seven hours".
"She was just insistent that she would only leave with us, and with that not being the case she just stayed there."
Eventually Ms Welton left the home with Ms Puriri, but without the children.
"It was just a stand off where the only way she would be able to leave was the family physically removing her. They weren't prepared to do so and we weren't making any progress. So the decision was made [that] I would leave with Barbara and the children remain in the house."
Ms Puriri said the children hold dual New Zealand/Algerian nationality.
She said negotiations had been "near impossible" and all avenues have been exhausted.
"Mohamed and I are attempting to negotiate some sort of resolution that we are both happy with. I think we've just reached the stage now where we want this over with. In the best interests of the children we just need to put aside our differences and move on with our lives.
"Hopefully we are able to come to a resolution that benefits the kids."
Despite being separated from her children, Mr Puriri had no doubt they were safe with her husband and his family.
"It's incredibly difficult. My son is going to be turning one next week, which is really upsetting. I'm the parent that spends every single hour of every single day with them, and not seeing them or not being allowed to see them is just really distressing."
A Ministry of Foreign Affairs and Trade spokesperson said the ministry was providing consular assistance to Ms Puriri and her children in Algeria.
"We've been involved in the case in providing assistance and advice since 2011."
New Zealand officials from Cairo had been in Algeria from September until recently to help Ms Puriri, he said.
The officials recently returned to Egypt but remained in regular contact with her, and had also spoken with her family, said the spokesman.
This afternoon Murray McCully's office issued a statement confirming he's requested a review of the events surrounding the nature of the assistance offered to Ms Puhiri.
"I have seen media reports suggesting that Ministry staff might have breached Algerian law in certain respects in attempting to assist Mihi Puriri," Mr McCully said.
"It seems to me the best way to deal with these criticisms is for the Ministry to report to me briefly on the actions taken so that we can see if any further lines of enquiry are called for."
Azzaoui, a former New Zealand and Pan Asian Boxing Association cruiserweight champion, came to New Zealand after competing in the 2000 Sydney Olympics.
He met Mihi Puriri soon after and moved to Northland, where the couple settled and started a family.
Kerikeri trainer Anthony Warren worked with Azzaoui for five years during his boxing career and the pair travelled the world together. He also knew Ms Puriri well, he said.
Since she left for Algeria her family had been trying to contact her and were very distressed about the situation, said Mr Warren, who had spoken to her father several times.
"They're deeply unhappy with her being over there."
The boxer was a strict Muslim and Islam was a "big part" of his life, he said.
Mr Warren hinted at ongoing issues between Azzaoui and his wife's family.
"Things didn't go too well with his family life. They went their own ways as far as his in-laws were concerned."
Another former trainer, who wanted to be known only as Rusty, said, "I think she was having a bit of a problem trying to be Muslim and their ways. I don't think she fully converted."
