Mr Azzaoui said her claims were untrue.
"Whatever she and her family are saying is not true. The fact is we came here for a holiday on August 7 during Ramadan [Muslim month of fasting] and after two months, Mihi decided to return home,'' he said.
Mr Azzaoui said he sent her back to Kaikohe without their children to sort out some papers for Green Acres, a cleaning franchise he ran in Kaikohe.
After spending two weeks in Northland, Ms Puriri returned to Mostaganem and his family warmly welcomed her, he said.
"She was leading a normal life with my family here. I told people we were very happy here and she even agreed for me to go to Australia and sign a boxing contract before she left for New Zealand.''
Mr Azzaoui said trouble flared when she returned to Algeria.
"She contacted this lady [New Zealand consul from Cairo Barbara Welton] in Egypt who later turned up with a court order and tried to take my kids by force.
"We were all shocked because we didn't know Mihi had spoken to her. There was nothing wrong yet she [Ms Welton] came from nowhere to control our lives.''
He said Ms Welton claimed his wife was not happy at her in-laws' place but, after angry protests from his family, she left without Ms Puriri or their children.
Police officers were present when Ms Welton tried to take Ms Puriri and their children, he said.
Mr Azzaoui said Ms Welton was staying in a hotel from where she called and apologised for interfering in the affairs of his family.
"Everyone knows in New Zealand that I was a boxer and I've spent a lot of time in the community training kids and running my business.
"We don't do the sort of things she [Ms Puriri] claims we did. If I did that ... if I held her against her will in my house, I would be jailed,'' Mr Azzaoui said.
His family was deeply upset with one-sided stories being fed to the public, he said.
Mr Azzaoui did not say whether he would come back to New Zealand or settle in Australia to pursue boxing.
In a video posted on YouTube last week, Ms Puriri made an impassioned plea for him to let her see their youngest child Zakaria on his first birthday.
A former New Zealand and Pan Asian Boxing Association cruiserweight champion, Azzaoui came to New Zealand after losing in the second round at the 2000 Sydney Olympics.
He met Ms Puriri soon afterwards and moved to Northland, where the couple settled and started a family.
A spokesman for Ms Puriri questioned what Mr Azzaoui said.
"The comments made by Mr Azzaoui are completely at odds with all previous comments he has made to Algerian media and others involved in this unfortunate matter,'' the London-based spokesman said.
"We consider that this is just more lies and misrepresentations by Mr Azzaoui. His comments that the New Zealand Consul to Cairo, Ms Barbara Welton, rang to apologise are just fanciful in the extreme.''