Abortion decriminalisation is likely to be back on the agenda in the next New South Wales parliament, with Labor, the Greens and a key independent signalling they will pursue it.

On Wednesday federal Labor announced a national sexual and reproductive rights strategy to improve access to contraceptives and abortion, and vowed to work with the states on decriminalisation.

Abortion remains in the Crimes Act in NSW, while South Australia designates abortions not sanctioned by two doctors as “unlawful”.

NSW Labor has not pledged to decriminalise abortion but will move on the issue in its first year of government if elected on 23 March.

“A Daley Labor government will refer the issue of abortion decriminalisation to the NSW law reform commission to allow the preparation of a well-thought-out bill which can then be considered by the parliament,” said shadow attorney general Paul Lynch.

The resulting bill would remain subject to a conscience vote for all Labor MPs, he said .

The Labor leader, Michael Daley, is pro-choice but has not indicated a strong personal view on decriminalisation since taking the top job late last year.

The premier, Gladys Berejiklian, who is also pro-choice, has previously said she was “open-minded on the issue”, though a spokesman said the Coalition had no plans to amend the relevant sections of the Crimes Act.

“Should a private member’s bill be introduced to the NSW parliament to repeal these offences, Liberal and Nationals members would be given a conscience vote,” he said.

Even if Labor were not elected, it is likely a bill in some form would come before the next parliament.

The Sydney MP Alex Greenwich, one of several crossbench MPs who could play a kingmaker role in the event of a minority government, has confirmed he will work with others on a draft bill later this year if re-elected.

“This is a long-overdue reform,” he told Guardian Australia. “Abortion should not be in the criminal code and I think there is growing commitment in the parliament to see this happen.”

The Greens also confirmed their intention to introduce a bill in the first year of the next parliament.

Unlawfully procuring an abortion in NSW is an offence punishable by up to 10 years’ imprisonment, while unlawfully procuring drugs or instruments for the purposes of an abortion is punishable by up to five years.

Abortions can be legally conducted under a 1971 interpretation of the Crimes Act by the NSW district court, known as the Levine ruling. Abortions are lawful where a doctor believes the procedure is necessary to preserve the woman from serious danger to her life or physical or mental health.

Prosecutions are rare, though in 2017 a Sydney woman was convicted and placed on a good behaviour bond after self-administering an abortion drug she bought online.

Labor’s policy follows similar moves by the Queensland party, which introduced legislation to decriminalise abortion after seeking recommendations from the state’s law reform commission. The Queensland parliament voted to legalise abortion in 2018.

One NSW Labor backbencher, the Summer Hill MP, Jo Haylen, said last month she would work across parliament to make decriminalisation happen if Labor were elected, and believed it would be possible to get the law changed. “The fact that NSW is the only state to have abortion in the Crimes Act is abhorrent,” Haylen said.

Labor’s national conference last year resolved that abortion should be “legal, safe, affordable and accessible” and should be treated as a health issue, but did not adopt a platform change to bind its MPs in favour of decriminalisation.

A previous attempt by the Greens to decriminalise abortion in NSW failed, after it was was voted down 25 to 14 in the state’s upper house in 2017.

A Greens upper house candidate, Abigail Boyd, said she was concerned that Labor’s plan to send the matter to the law reform commission could result in some restrictions remaining, “so we’ll end up with abortion still being a crime in certain circumstances, or some sort of new legislation that still restricts women’s right to choose”.

The original Greens bill was supported by a range of health organisations, including the Royal Australian and New Zealand College of Obstetricians and Gynaecologists and Family Planning NSW, but was opposed by the Catholic church.

Berejiklian has also signalled her intention to introduce laws to better recognise the loss of a foetus during a criminal act if re-elected, after a woman who was heavily pregnant with twins was killed in a car accident last year.

She has pledged any new laws would not affect existing abortion laws.

The Christian Democrat MLC Fred Nile has tried unsuccessfully for five years to pass a bill, known as Zoe’s law, which would make it a crime to seriously harm or kill a foetus in certain circumstances.

Labor’s deputy leader, Penny Sharpe, said in recent years the upper house had been generally pro-choice – supporting safe access zones around clinics and not passing Zoe’s law – but she said she there was some uncertainty about the next term.

“My concern is just what is the makeup of the upper house, with so many rightwing groups vying for spots at this election,” she said. “No one seems to know how that will end up.”