The women and equalities minister, Penny Mordaunt, has signalled her determination to change the “appalling” abortion laws in Northern Ireland a day after the two Conservative leadership rivals ruled out reform on the issue.

Boris Johnson and Jeremy Hunt were accused of pandering to religious fundamentalists in the Democratic Unionist party by claiming that abortion rights were a matter for the devolved assembly if power sharing was restored.

But Mordaunt, who is also the defence secretary and is backing Hunt in the contest, said the issue needed to be resolved in Westminster.

Speaking to BBC Radio 4’s Today programme, she said: “I think paucity of care that women have endured in Northern Ireland is the most appalling thing and it must change.”

She predicted the government would have to intervene soon; a court is expected to rule imminently that Northern Ireland’s ban on abortion is incompatible with human rights rules.

Mordaunt attempted to gloss over her differences with Hunt on the issue. She said: “He is right, but what I am saying is also right. The reason why this hasn’t been dealt with to date is because this is a devolved matter and we take devolution seriously. But it has been shown, and we will soon see what the court’s ruling is on this, that what has been happening is not compatible with an individual’s human rights.”

She added: “If we have this ruling by the court I think government will act. Certainly that has been the indication from the Northern Ireland office. But if government did not, parliament would, and clearly all members of parliament, including prime ministers, would have a free vote in that.”

Mordaunt also conceded it was “fair criticism” to say the government had kept the public waiting too long for it to carry out its plans on social care. “People have been waiting for promises on care for a long time,” she said.

Earlier, Mordaunt promised to “give new welly” to tackling gender inequality through a roadmap aimed at empowering women from school to retirement.

She said the plan would “define and guide” how to tackle the barriers women face.

Gender Equality at Every Stage: a Roadmap for Change points out that girls are more likely to get a top grade in maths GCSE, yet boys are over 50% more likely to take maths at A-level. And women enter the labour market with higher qualifications than men – but earn less per hour from the start.

Speaking to BBC Breakfast, Mordaunt said the plan would include pilot studies in schools to address why girls are “nudged in particular directions” on subjects they take and career paths they follow.

She said the roadmap also pledged measures for more equal parental leave; employment rights and paid leave for carers; and measures to ensure pension provisions continue for women after a divorce.

Mordaunt expressed frustration at the lack of progress. She said: “The question is, why haven’t we got further? Why aren’t we focused on a woman and everything that she needs in life to thrive? If we don’t look after carers, if we don’t value unpaid care work, if we don’t allow those people to remain economically active there’s a cost of business, and there’s a cost to society as well.”

She added: “We’ve got to do these things and the roadmap, plus the new welly that we’re giving this whole agenda in the Cabinet Office will will enable us to get some of these things done.”

Sarah Ewart, a Northern Irish woman who was forced to travel to England for a termination of her pregnancy and has legally challenged the abortion ban, welcomed Mordaunt’s intervention.

Backed by Amnesty International, Ewart said she was encouraged by Mordaunt’s intervention in the debate.

She said: “We shouldn’t have to fight through the courts to have our rights realised. Experiencing something as painful as I did and then having no option but to go through the ordeal of the courts is emotionally draining. Northern Ireland’s archaic abortion laws have left women like me suffering for far too long.

“We met with Mordaunt previously to discuss the situation in Northern Ireland and welcome her comments. We hope the government listens to women like me who have called on Westminster to legislate. We will keep fighting, alongside Amnesty, until change happens.”

In 2013 Ewart was told that her unborn child had anencephaly and had no skull. But under the law in Northern Ireland abortions in cases of fatal foetal abnormalities are still illegal. Rape and incest victims made pregnant through sexual violence in Northern Ireland are also not allowed to have abortions in local hospitals.