"I do welcome the ongoing negotiations in relation to the bill, and in particular those amendments regarding conscientious objection (for medical practitioners), to which I previously moved an amendment in the Legislative Assembly," Dr McGirr said.

A group of three MPs, including Wagga-born Liberal MLC Matthew Mason-Cox, called off their attempt on Tuesday morning to bring a leadership spill motion against Premier Gladys Berejiklian.

A statement from the MPs claimed they had "received confirmation that further concessions will be forthcoming on amendments to the Abortion Bill".

The MPs also stated they would "continue negotiations prior to the debate in the upper house".

Mr Mason-Cox did not respond to a request for comment on Tuesday.

The most high-profile of the three MPs challenging the Premier, former minister Tanya Davies, has called for changes to the bill to ensure doctors who opposed abortion would not have to refer their patients to another practitioner.

Dr McGirr sought a similar change to the legislation during debate in the lower house last month.

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As an independent, Dr McGirr has no role in the process of Liberal Party MPs electing their leader but he expressed confidence in Ms Berejiklian.

"I have no reason to question the Premier and the government in supporting the Wagga Wagga electorate," he said.

During debate on the abortion bill on Tuesday night, an amendment to reduce a period for easier abortion access from 22 weeks to 20 failed to gather support.

Wagga-based Nationals MLC Wes Fang, who has said he will support the overall legislation, told Parliament he would not support the 20-week amendment.

"Initially I was inclined to support these amendments. The 22-week trigger had given me some concern but I sought advice from the Royal Australian and New Zealand College of Obstetricians and Gynaecologists and the Australian Medical Association," Mr Fang said.

"It was on their advice that the 22-week trigger not only requires two doctors for approval but also severely limits the number of hospitals in which the termination can be performed.

"That raises issues around the provision of health care in rural and regional communities that do not meet those standards and creates a barrier for rural and regional women receiving similar services that women in metropolitan areas may receive.

"It is on that basis and that basis alone that I am not able to support these amendments."

However, a minor amendment to rename the bill was passed, meaning that the legislation will have to return to the lower house if the entire legislation is backed by a majority of MLCs.