The bill would for the first time allow women who are up to 12 weeks pregnant to have abortions performed by a qualified doctor should they request it for any reason.
They would not need to show they have been raped or that the pregnancy threatens their life or that the unborn baby would be born disabled.
However, it would still be illegal for women who are more than 12 weeks pregnant to have an abortion.
The Criminal Code currently criminalises abortions across the board regardless of the age of the foetus.
The cabinet-sponsored bill was one of two debated in the House of Representatives yesterday.
The other draft, initiated by the Move Forward Party (MFP), proposed allowing abortions to be performed on women up to 24 weeks pregnant.
In the end, the House voted in favour of the cabinet-sponsored bill and it will now be put to a scrutiny committee in parliament.
Currently, the law forbids women self-performing an abortion or allowing someone else to perform it.
Both offences are punishable by up to three years in jail, a fine or up to B60,000 or both. If the bill passes, the law would specify punishments for abortions carried out on pregnancies beyond 12 weeks.
The debate went on in the chamber while outside, activists called in vain for the lawmakers to back the MFP bill, which they described as liberal and “open-minded”.
The bill states that the phrase “pregnant women” be dropped in favour of “pregnant individuals” as some female-to-male transgender people remain able to conceive.
Sulaiporn Chonwilai, an independent researcher and adviser to the Women Help Women (WHW), said the group had earlier campaigned for pregnancies beyond 24 weeks to also be made legal, although agreeing to strict conditions.
From her experience in advising and helping pregnant women, Ms Sulaiporn said 20-30 of them had sought to have abortions after they were 12 weeks pregnant.
That showed, she said, that the cabinet-sponsored draft may not reflect reality or be practical.
She said WHW also wanted MPs to cancel Section 301 of the Criminal Code which punishes women for self-performing the abortion or consenting to have someone else performing it.
The proposed amendments would enable pregnant women to have a safe abortion procedure, said Ms Sulaiporn.