Democratic Unionist leader Arlene Foster has said some nationalists will now vote for her party following Ireland's overwhelming vote in favour of abortion law reform.
The DUP opposes changes to abortion law in Northern Ireland, while nationalist Sinn Féin is in favour of reform.
Mrs Foster said some Sinn Féin voters backed her party's stance.
But Sinn Féin's former finance minister said he doubted nationalists would vote for the DUP.
Following the Republic of Ireland's referendum to liberalise abortion law, Northern Ireland will soon be the only part of either the UK or Ireland where abortion is illegal unless there is a serious risk to a woman's life or health.
Sinn Féin leader Mary Lou McDonald and deputy leader Michelle O'Neill are in favour of change to abortion laws in Northern Ireland, and attended the official abortion referendum result announcement at Dublin Castle last Saturday.
They held up a sign on stage, saying: "The north is next."
South Belfast MLA Máirtín Ó Muilleoir told the BBC he did not see a scenario where nationalists or republicans would switch to voting DUP based on the issue of abortion.
"It is highly unlikely that any republican is going to vote for a party which is so vehemently against civil rights and human rights as the DUP and I think that is true for nationalism as well.
"Everybody is entitled to vote as they wish, but after that it's not really about the constitutional issue.
"There are many nationalists, republicans, unionists and loyalists here and in my view they will have their own opinions around termination, around abortion, around trusting women and at the end of the day on the constitutional issue they will remain true to their beliefs."
Earlier his party colleague Linda Dillon told the BBC's Sunday News show: "Not everybody agrees with the position, and I understand that, but most of the people I've spoken to agree with most of Sinn Fein's policies and will continue to vote."
The party supports abortion in the cases of rape, incest, sexual abuse and fatal foetal abnormality.
In an interview with Sky News, Mrs Foster said many anti-abortion voters in the Republic of Ireland were in shock.
"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 we're the only party that supports the unborn," she said.
"There are many people who are shocked in the Republic of Ireland. 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 who feel very disenfranchised, who feel very alone, who don't feel that anyone speaks for them any more."
Labour MP Stella Creasy also said that the result of the referendum reflects the importance of listening to communities.
The politician, who has called for MPs to repeal the 1861 Offences Against the Person Act, which makes abortion illegal, said Mrs Foster is "the only woman with any choice over abortion in Northern Ireland".
She is hoping to use amendments tabled to a forthcoming domestic violence bill to force a vote on the issue at Westminster.
Following Mrs Foster's comments, the DUP's North Antrim MP Ian Paisley said that he had received a letter from a priest in his constituency.
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. https://t.co/Ix3uzw4x9Q— Ian Paisley MP (@ianpaisleymp) June 3, 2018