At present, those aged under 16 are able to have information restricted from anyone if its deemed "the disclosure of that information would be contrary to that individual's interests", according to Section 29 (1)(d) of the Privacy Act 1993.
"As a family we are standing together to see a change for parental rights. We do not want other families to go through the pain and suffering we have had to endure," Mrs Kieft told the Justice and Electoral select committee today.
"[My daughter] went from being a happy...to emotionally unstable with extreme highs and extreme suicide lows. We wondered what had happened."
Mrs Kieft said her daughter's behaviour and eventual suicide attempt greatly affected her siblings, and the family was "turned upside down".
"There were times where me and my husband were actually afraid to even go to sleep, because we weren't sure what we were going to wake up to.
"I know what my girl had to go through, and she had to go through it alone. Lack of parental notification meant [she] was denied the support of her family. And we were robbed of the ability to properly support and parent our child."
All members of the committee praised Mrs Kieft for her bravery in sharing her story, and in lodging the petition.
Labour's justice spokeswoman Jacinda Ardern said there was no question that current practice had failed the family at almost every step.
"The things that are meant to happen in the system didn't happen for your daughter...she should never have been coerced, she always should have been given options and access to trained counsellors."
Ms Ardern said GPs who had spoken to the committee on the issue said they worked very hard to convince a young woman to bring in her parents in such a situation, but this didn't happen in this case.
Doctors had also reported of seeing young women who had been harmed when their family found out they were pregnant, Ms Ardern said.
"So this is what we've got on the one side, on the other side we have got stories like yours. So we are trying to balance those two things."
National MP Jono Naylor said counsellors had told the committee that best practice was to counsel young women to involve their family, unless they judged that such advice could harm the teenager.
Mr Naylor said that did not appear to have happened in the case of Mrs Kieft's daughter, and the system had failed.
Mrs Kieft's petition is the second times such changes have been pursued.
In 2004, the Care of Children Act was passed. Amendments by Judith Collins, Murray Smith and Dale Jones sought to make parental notification compulsory, but they were defeated by considerable margins.
Family Planning chief executive Jackie Edmond has said any changes would be a sad day and a "very backwards step" for New Zealand.
"We've already got a very restrictive abortion law that's outdated and not fit for modern day."
Where to get help:
• Lifeline: 0800 543 354 (available 24/7)
• Suicide Crisis Helpline: 0508 828 865 (0508 TAUTOKO) (available 24/7)
• Youth services: (06) 3555 906
• Youthline: 0800 376 633
• Kidsline: 0800 543 754 (4pm to 6pm weekdays)
• Whatsup: 0800 942 8787 (1pm to 11pm)
• The Word
• Depression helpline: 0800 111 757 (available 24/7)
• Rainbow Youth: (09) 376 4155
• CASPER Suicide Prevention
• Pregnancy Counselling Services: 0800 773462
If it is an emergency and you feel like you or someone else is at risk, call 111.