Gladys Berejiklian 'relaxed' about NSW abortion bill debate after tumultuous week in NSW politics

NSW Premier Gladys Berejiklian insists she is "entirely relaxed" about the debate on the abortion bill after an amendment demanded by rebel MPs was rejected in the upper house.

Transport Minister Andrew Constance, meanwhile, says MPs should "park the politics" and focus on the issues.

Liberal MPs Tanya Davies, Matthew Mason-Cox and Lou Amato announced and then called off a leadership spill motion against the premier this week over her handling of the private member's bill to decriminalise abortion.

Their statement said it had previously been made clear to the premier that an "absolute minimum" of four key amendments were needed to ensure "continued membership of the Liberal Party room", including a prohibition on sex selection abortions.

An amendment to ban sex-selective abortions was rejected in the upper house late last night, with members voting against the change 26-15.

However, Finance Minister Damien Tudehope, who moved the failed amendment, has now introduced another on the issue.

When asked if she was concerned about MPs defecting from the Liberal Party because of the failed amendment, Ms Berejiklian said she was "pleased that a number of amendments were passed in the upper house".

"There's still a number of amendments to be debated. I wouldn't jump ahead of what the upper house is considering and debate's still continuing so I don't want to pre-empt any discussion," she told reporters on Thursday.

The Premier said she was "entirely relaxed" about the process "because we live in a democracy and people are allowed to express their views".

She did not feel betrayed by the threat of a spill motion and she "absolutely" wanted Ms Davies to remain in the party.

"Some days in the office are easier than others and we take it all in our stride," Ms Berejiklian said.

Mr Constance, who supported the bill in the lower house, said MPs should "park the politics, focus on the issues".

"I'd ask Tanya Davies to be mindful and respectful of the conscience vote that we all have to go through, and also be mindful of the fact that the premier gave everybody that opportunity," he told reporters on Thursday.

Mr Tudehope's rejected amendment sought to ban terminations that medical practitioners know, or ought reasonably to know, are being performed for sex selection.

It had attached a maximum six-month prison sentence for the offence.

Labor MP and abortion bill co-sponsor Penny Sharpe opposed that amendment, saying there was a worldwide problem regarding sex-selective abortions but no evidence it was taking place in NSW.

The upper house has passed several amendments, including one clarifying that doctors must provide appropriate care to babies born alive after a termination.

They spent hours debating amendments on conscientious objection before agreeing tonight to one moved by Nationals MP Niall Blair, who said it would ease the obligation on practitioners with such an objection.

"Rather than asking the doctor to refer the patient to another doctor who they know will not have a conscientious objection... the amendment puts in another step by enabling the doctor to refer the patient back to NSW Health," Mr Blair said.