DUP leader Arlene Foster has said that she has been contacted by nationalists and republicans who said that they will vote for the DUP because of their anti-abortion stance.
Mrs Foster told Sky News that they "believe that we're the only party that supports the unborn."
She revealed that she had also been contacted by a number of people in the Republic of Ireland following the decision to repeal the Eighth Amendment to the Irish Constitution.
The Republic of Ireland will now introduce abortion legislation in the coming months.
Sinn Fein have called for abortion legislation to be introduced in Northern Ireland, while Mrs Foster said that the referendum in the Republic would change nothing in Northern Ireland.
Speaking after the referendum Taoiseach Leo Varadkar said that women from Northern Ireland may be able to access abortion services in the Irish Republic.
"I have had many emails as you would expect, as the leader of the DUP over the weekend and since," Mrs Foster said.
"I have had emails from people in the Republic of Ireland feeling very disenfranchised and can't quite believe what has happened.
"I have had emails from nationalists and republicans in Northern Ireland not quite believing what is going on and saying, they will be voting for the DUP because they believe that we're the only party that supports the unborn."
Mrs Foster said that a sizeable majority of people in the Republic feel left behind following the result of the referendum.
"There are many people who are shocked in the Republic of Ireland today. And whilst I completely acknowledge the result that happened last Saturday that doesn't take away from the fact that there's a substantial minority of people in the Republic of Ireland today who feel very disenfranchised. Who feel very alone. Who don't feel that anybody speaks for them anymore," she said.
"I think people need to be very much aware of that, because we've seen with the referendum recently, the referendum in the UK, around Brexit, of course, the referendum in Scotland, when you have these big constitutional questions and the people on the losing side - if you like - feel very much that they've lost something very significant.
"And I think that needs to be acknowledged."
The Fermanagh and South Tyrone MLA said she had not been surprised that people were considering voting for the DUP over the abortion issue.
“People vote for different reasons and I think that’s very clear. For some people, this is the number one issue for them when it comes to casting their vote and I think people need to understand that in the wider UK," she said.
"It is such a big issue here in Northern Ireland. Obviously some people don’t see it as such a big issue and vote for other reasons but I think it would be wrong not to acknowledge that there those in my own constituency and right across the whole of Northern Ireland who feel so very strongly about this issue that they will cast their vote on that basis.”
The DUP leader said that it was up to the Assembly to decide the future of Northern Ireland's abortion legislation.
"Of course what happened last weekend was in relation to the constitution of the Republic of Ireland. It was about repealing the constitutional bar on abortion and the result was what the result was," Mrs Foster said.
"We don’t have a constitutional bar on abortion. The issue should be one that is debated in the Assembly. It’s one that rests with the devolved administration and that’s where we should have the discussion."
Speaking on Twitter following Mrs Foster's comments North Antrim DUP MP Ian Paisley said he had been contacted by a local priest who supports his party's stance.
"I have a letter from a local priest in my constituency thanking the DUP for its stance on these issues and assuring me that he is urging his parishioners to vote DUP because of the stance we take on social matters," he wrote.
In response to Mrs Fosters claims a Sinn Fein spokesperson said that abortion was not a "unionist versus nationalist issue".
"It affects women from all communities," the spokesperson said.
"It is about coming at the issue with compassion and respect, trusting woman and their doctors. While there are some with strongly held views, it is not credible to suggest that it will make republicans become unionist.
"Just as it would not be credible to suggest that unionists who support and trust women on this issue will become republicans. It is simply a wrong that needs put right."