Under thenew law, the decision on whether to get an abortion will be up to the woman, in consultation with her doctor, until she is 20 weeks pregnant.
After that, the person performing the procedure will have to "reasonably believe the abortion is appropriate with regard to the pregnant woman's physical and mental health, and wellbeing".
Abortion is currently a crime in New Zealand, but exemptions mean women can still get access if two doctors agree a pregnancy would put them in physical or mental risk - a process that's been criticised as both slow and stigmatising.
The bill will be voted on in a conscience vote in Parliament, rather than along party lines, with its first reading in the house on Thursday.
National Party MP for Rotorua Todd McClay said he wanted to carefully read the legislation, then consult with the wider Rotorua electorate and community before making his decision.
"I am considering supporting it in the first reading so that all New Zealanders can put their views before Parliament."
Waiariki MP Tamati Coffey said he would support the bill going to the select committee.
"While I want to see the finer details of the legislation, I support change in the bigger picture."
He said the current law treated women like criminals for seeking an abortion and he would like to see the procedure regarded as a health issue, not a criminal issue.
He welcomed the debate that would come from the abortion law reforms, along with the discussion that came from the other "meaty topics" currently being worked through such as the End of Life and cannabis bills.
Rotorua-based deputy leader of New Zealand First Fletcher Tabuteau has been contacted for comment.