National Party leader Simon Bridges will back abortion law reforms when they come up for a first vote in Parliament this week, but says he wants more safeguards put in.
The most significant change will see the current requirement for women to get clearance from two doctors on physical or mental health grounds dropped, in favour of open access until 20 weeks' pregnancy.
After 20 weeks, the medical practitioner performing the procedure will have to give approval.
The law is expected to pass its first reading in the House on Thursday.
It will be conducted as a conscience vote, meaning MPs vote individually, rather than along party lines.
Bridges has generally voted conservatively on conscience issues in past. On Tuesday he said he would see the abortion reform through a first reading in order to see what changes could be made by the Select Committee Process that follows.
But he said he wanted more safeguards put in place for late-term procedures.
"Effectively the [current] position pre-20 weeks of gestation is one where law and practice should match. They haven't, so that's the right position," he told reporters.
"[But] it seems to me there should be significantly stronger safeguards on that post-20 weeks and late term ... It'll be for the Select Committee to go through that and I'll be watching that very closely."
Bridges said he agreed abortion should be treated as a health issue, but said it was "more complex" for late-term procedures.
Other MPs who have voted conservatively in past have also said they would also keep an open mind.
Labour's Aupito William Sio, who represents the South Auckland electorate of Māngere, said he was leaning towards seeing the bill through its first reading.
"I'm really keen to be listening more to our young people and to the women in our communities – mostly because I've had to deal with a number of issues as the local member of Parliament where young women have not felt supported by their families and their partners," he said.
"It is a life and death issue and there are traditional views around life and who holds power to life and the value of life. But we've got to temper that, in my view, in terms of how do you make sure that the health of the mother and the unborn baby are protected."
Meanwhile, National's Chris Penk on Monday said the law would liberalise abortion "right up to birth".
Justice Minister Andrew Little refuted that as an "extremist" claim.
"It is simply not what happens. Women do not seek abortion at the point of birth. That is a ridiculous proposition. It's sort of scaremongering. But it's dumb," Little told reporters.
"We should have a good debate about this because it's an important topic, but it would be good if we could stick to the facts."
There were about 13,000 abortions performed in New Zealand last year, according to Statistics New Zealand. Only 57 of those took place after 20 weeks into the pregnancy.
Little said there were none even close to full term.
If the bill passes its first reading, it will go to a special Select Committee set up to consider submissions and possible changes.
Opponents, such as the conservative Family First lobby group have vowed to fight it, while backers, such as Family Planning, say they want it to go further.
Little said the plan was to have the bill in law before next year's election.