Of the 15,863 abortions last year, 8050 were for women in this age group.
The Abortion Law Reform Association of New Zealand (ALRANZ) says contraception should be freely available to all women.
"If we want to lower the abortion rate, the way to do it is to not restrict abortions," member Alison McCulloch said.
"It is to ensure there are fewer unplanned and unwanted pregnancies [and] the way to do that is to increase access to contraception and to have education programmes."
A young Rotorua mother, who decided to terminate after accidentally becoming pregnant, spoke to The Daily Post about her ordeal.
"I found out I was pregnant [a few] weeks ago ... and went straight to the doctor and set up my abortion because I've already got two babies under 2 and I couldn't cope because I'm a single mother."
The 24-year-old, who spoke on condition of anonymity, said the decision to abort was one of the hardest things she had been through.
"The [doctors] did explain to me that I had other options like adoption.
"They asked me why [terminate] and I said it's because I have two young babies already.
"They asked me why I didn't want to do adoption and I just told them it would be hard for me to carry for nine months and get attached to ... my baby, and it would be hard for me to just let it go."
The mother said termination was not something any woman should have to go through.
"Avoid unplanned or unwanted pregnancies and just get yourself sorted out," she said.
Exactly one week after her termination, the 24-year-old had a Jadelle contraceptive device implanted, which would prevent pregnancy for up to five years.
Under the Government's controversial new welfare reforms, free long-term contraception is being offered to beneficiaries.
Pro-life protesters recently sent threatening messages to staff at a Southland abortion clinic.
Reports of name-and-shame tactics at the Invercargill clinic, which opened last month, have been condemned as vigilante extremism by politicians and ALRANZ.
"Everyone is entitled to say what they want to say, but it's not fair ... if they don't know the situation," the young mother said.
Voice for Life New Zealand says that women need more information when they visit a doctor for a termination.
"Our view is free contraception will not lower the [termination] rates," administrator Steve Jaunay said.
"It hasn't in the past and it won't in the future.
"The issue is that the choice is not fully informed, and that's our concern," he said.
Mr Jaunay said doctors needed to disclose information to women about research linking mental and emotional disorders with abortion.
