Northern Ireland's health minister is to meet the Public Prosecution Service over potential prosecutions of health care staff involved in abortions.
Edwin Poots has also offered to meet a couple whose unborn twins have a serious abnormality.
The babies' mother had urged Mr Poots to allow her to have an abortion in Northern Ireland.
Mr Poots said: "The circumstances in this case are being fully explored from a legal perspective."
The woman, who wanted to be named only as Laura has been told her girls have anencephaly, a severe brain abnormality.
She is 22 weeks pregnant. Foetal abnormality is not a ground for abortion under Northern Ireland law.
Laura said she felt "let down by her country" at having to leave to have the abortion.
"I'm not going to be near my family, I'm not going to have any of my family's support," she told BBC Radio Ulster's Nolan Show.
"I have a hard enough thing to go through at the minute, finding out I have twin girls with the same condition who are going to have absolutely no outcome of life whatsoever.
"To make that decision in the first place (to have an abortion) was one of the hardest decisions I've ever had to make in my life.
"I think it's horrendous the fact that I have to go to a different country where I don't know anybody and have to go through something like that."
Laura said she only found out she was expecting twins after her five-month scan; the next day she found out they had anencephaly and would have "absolutely no form of life whatsoever".
"I don't think I could ever go full term and have them in your arms for a couple of hours and have to watch them pass away is just something I don't think I could cope with," she said.
"They only have a heartbeat, that's all they have, the only thing that's keeping them alive is me."
She said there was also a strong chance the babies would die in the womb.
The twins' father, Chris, added: "We would like to be given the option, like any family in our position, to get the treatment that we require in our own country and have our families around us."
In a statement, Mr Poots said: "This couple have my deepest sympathy. This is an extremely traumatic time for them and I want to be assured that they are receiving all the support and care that they need.
"I can offer my assurances that I will listen to the voices of those affected by such a difficult situation.
"I am willing to meet with this couple if they so wish and have asked my officials to contact them to offer a meeting.
"The issue of potential prosecutions for health care staff involved in abortion has been raised, and I will meet with the Public Prosecution Service to discuss this matter".
On Wednesday, another woman, Sarah Ewart, contacted the Nolan Show to highlight her experience.
She had to travel to England for an abortion because her baby was also diagnosed with anencephaly.
Law to be examined
On Thursday, Justice Minister David Ford said he was committed to bringing a paper to the Northern Ireland Executive looking at issues around the termination of pregnancy.
"That arose out of the previous issue on the discussion of the Marie Stopes clinic," he said.
"I have written to the minister of health suggesting it should be a joint paper, because there are issues of both criminal law and health and social care issues.
"It seems to me that what we've had highlighted yesterday and today is the need that we perhaps need to widen out that consultation to look at difficult issues like foetal abnormality to see if where the law is currently drawn is in the right place."