MPs are debating the proposed abortion law changes in Parliament in the legislation's first reading.
It will be a conscience vote, so MPs will be able to vote according to how they feel about the issue - they won't be voting on party lines.
National MPs such as Paula Bennett and Amy Adams have expressed support for the Bill, while National leader Simon Bridges has said he would like to see some changes made to the legislation.
"I do believe women have the right to choose," Bennett said in Parliament on Thursday.
The Greens have long-supported abortion law reform. Green MP Jan Logie said women should be trusted to make their own decisions about their bodies.
National MP Jo Hayes said she will oppose the legislation, while National MP and Deputy Speaker Anne Tolley said she will support it because she believes abortion "is not a criminal act".
Labour MP David Parker said despite being brought up in a Christian environment, he believes women should have the right to choose.
New Zealand First leader Winston Peters has suggested that the proposed reforms should be put to a referendum.
He said this week that pushing for a referendum was on the cards, and has confirmed that his party will seek to add a referendum to the proposed law at the select committee stage.
The Bill was put forward by Justice Minister Andrew Little.
He announced the legislation on Monday which would make abortion legal for women and be treated as a "health issue".
The legislation, which would make changes to the Crimes Act, proposes removing any statutory test from doctors for a woman who is not more than 20 weeks pregnant.
As it currently stands, abortion is an offence under the Crimes Act, and women have to use a loophole to make it legal.
Two medical practitioners have to agree the pregnancy would put the women in physical or mental danger to allow her to proceed with the abortion.
Under the proposed law, a woman who is more than 20 weeks pregnant would require one doctor to believe the abortion is appropriate with regard to her physical and mental health, and well-being.
Doctors will also have to advise women of the availability of counselling services if they are considering an abortion or have had an abortion, although counselling will not be mandatory.
Women will also have the right to be referred to a health practitioner who can provide the service, if her doctor objects on the grounds of conscience.
It will remain an offence for unqualified people who attempt to provide abortions or supply the means for them. It will also still be illegal harm to a pregnant woman, and in doing so, cause the death of a fetus.