Parker, who appeared before the Parole Board on Friday morning, is due back before the board in March.
He may be placed on a release-to-work programme before that date, if a place becomes available.
It emerged during the hearing, however, that police had summoned Parker on fresh charges just this week.
A police spokesman told RNZ the 49-year-old would appear in the Christchurch District Court early next month on seven charges, including indecent assault and sexual violation.
The charges arose from allegations of historical sexual assault against one victim which had been under investigation since early last year.
Police would seek to have the case transferred to Kaitāia District Court.
Parker told the board he was devastated by the new charges, which he was told about on Wednesday.
His lawyer, Alex Witten-Hannah, said police had assured him just two weeks ago no new charges were pending.
Parker, who was deputy principal at Pamapuria School, near Kaitāia, is serving a term of preventive detention, which means he can be released only when the Parole Board considers it safe to do so.
He was jailed after admitting 74 charges representing at least 300 occurrences of indecent acts, unlawful sexual connection and sexual violation involving boys aged 9 to 16.
The offences occurred between 1999 and 2012.
Parker looked little different when he appeared before the board today than he did in Kaitāia District Court almost 12 years ago.
He was nervous about the presence of media at the hearing, and tearful when he spoke of the effect he had had on his victims.
"I'm mortified now, every day when I wake up and I remember what I've done. I loved my community, and I still do, but I betrayed their trust, and that's very hard to live with," he told the board.
"It's awful to think that I took away their childhood, I took away those first experience that they should have had… There was so much publicity they [the victims] couldn't even go to school. It must have been absolute hell for them."
Asked by board member Chris King how his offending started, Parker said he had been brought up in Christian household with strong beliefs, but always knew he was attracted to the same sex.
"In those times that wasn't okay with our church or our family, so I learned to hate that part of myself and wished I could be different."
He had since come out, including to his family, and now realised they loved and supported him regardless.
Parker said he had felt confused and excluded around adult men, and sought approval from everyone else.
He felt particularly accepted by children, who gave him a sense of love and belonging.
However, he had distorted that, and turned it into "something sexual".
He said he genuinely loved teaching and did not seek out the profession to allow him to prey on vulnerable children.
Parker accepted he would never teach or work with children again.
He said he was committed to the treatment and, once released, would stay in the South Island, to avoid encountering and re-traumatising his victims.
"I'm not fixed, but I know now I can manage it, I know the warning signs, I know the risks, and I'm absolutely determined [not to reoffend]."
A prison staffer told the board there were no issues with Parker, who was always polite and currently working in Rolleston Prison's administration block.
The board declined parole but King said he hoped Parker would get into a release-to-work scheme before his next hearing in March.
That was an important part of the process and a chance to see if Parker could apply the lessons he had learned during treatment.
Parker, then aged 38, was sentenced in 2013 to preventive detention with a minimum non-parole period of seven years.
His case was described by the Crown at the time as "without comparison in New Zealand history", and the damage he had done to his victims and the wider community as "incalculable".
Justice Paul Heath said Parker's actions had damaged the trust not only of his pupils and their families, but potentially the trust all parents placed in teachers.
He had sentenced Parker to preventive detention because he was not satisfied the community could otherwise be protected when he was eventually released.
At the time police praised the "heroic courage" of the first boy who spoke up about Parker's abuse, and refused to back down.
Concerns were first raised in 2009 about Parker and his habit of inviting boys to stay at his rural property.
He was warned by police but the court was told his behaviour only escalated from that point.