Concerns from conservative Coalition MPs including Andrew Hastie and Barnaby Joyce about paid parental leave applying to late-term abortions elicited “a bit of horror” from women in the party, according to Jane Hume, as Sussan Ley and senior figures rejected the claims from rightwing figures.

Ley branded as “insensitive” concerns raised by some colleagues about the potential for women to seek late-term abortions in order to access paid parental leave. The shadow minister for women, Melissa McIntosh, said: “I’ve never heard of a woman doing that.”

Hume told Sky News: “We shouldn’t be using straightforward legislation as some sort of Trojan horse for personal opinions on this. I thought it was an unnecessary distraction and perhaps a bit of an error of judgment.”

The debate comes from federal parliament’s consideration of “Priya’s law”, an amendment to the Fair Work Act that would protect employer-funded paid parental leave for parents of a child who is stillborn or dies.

The bill has passed parliament with bipartisan support from the Coalition, but a number of rightwing members in the House of Representatives last week and in the Senate on Monday – including Hastie, Joyce, Matt Canavan, Alex Antic, Jacinta Nampijinpa Price and Sarah Henderson – initially raised or backed concerns about abortion.

Hastie, a Liberal leadership aspirant seen as a potential successor if Ley loses her position, praised the bill’s “noble” intent but said “I do have a question about the unintended consequences of this bill and it applies to late-term abortions … It’s no secret that I am opposed to late-term abortions.”

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The Liberal MP Tony Pasin, a Hastie ally, said he was concerned the bill would “treat an intentionally late-term aborted child in the same way as it would a natural stillbirth or a baby who dies shortly after birth” and claimed parental leave “shouldn’t be available to people who don’t wish to become parents”.

Medical experts pointed out the vast majority of later terminations are forced by major health issues.

“Losing a baby after 20 weeks is losing a baby. We should treat anyone who loses a baby with compassion, instead of playing politics with people’s emotions and people’s distress,” said Dr Nisha Khot, the president of the Royal Australian and New Zealand College of Obstetricians and Gynaecologists.

Antic, Nampijinpa Price and Henderson voted for an unsuccessful One Nation amendment that would withhold paid parental leave in the case of an “intentional termination”; the Coalition’s Senate contingent backed Canavan’s unsuccessful amendment to exempt intentional terminations except in the case where a termination was to protect the health of the mother. The bill eventually passed without amendment.

Speaking after the bill’s passage on Monday, the workplace relations minister, Amanda Rishworth, said the law “is not about late-term abortion” and she was “disappointed that some senators tried to make it something that this is not”.

On Wednesday, Ley was asked about Hastie’s comments on ABC radio.

“We should be supporting women through tragic events where a baby is lost. Losing a baby is one of the most difficult things that can ever happen to a mother and to a family. As a mother and a grandmother, this is very personal. So any commentary about this bill applying in other contexts is insensitive,” she said.

Ley said she was “not talking about individuals in my party room or individual comments”, but added: “The last thing I’m going to do is issue judgments on mothers and [I’m] certainly very supportive of the bill, as is my team.”

Hastie’s office was contacted for comment.

McIntosh defended the right of MPs to raise concerns about conscience issues, though welcomed the passage of Priya’s Law.

“I think about the families, and we’ve all got friends and families who’ve lost children so late, and I can imagine how much it stirs emotional turmoil in people,” she said.

“So that was their decision. And I hope we can move on from that.”

Pressed on the issue raised by Hastie, Joyce and others, McIntosh added: “Have you ever come across a story where a woman has done that?

“I know that Andrew Hastie is a man of faith, so that’s their position, but that bill did go through, and I hope it does bring some comfort to families that would be very traumatised.”

Hume, demoted to the backbench but a former minister for finance and women’s economic security, was also critical of the comments. She said she and many inside the Liberal party supported a woman’s right to choose.

“I think that there was a bit of horror from many of the women in our party that this intervention was at all necessary,” Hume told Sky.

“This is a very serious and deeply personal issue. I don’t think we needed to politicise this whatsoever.”