DUP leader Arlene Foster has warned there will be less focus on Stormont talks on restoring power-sharing if a general election is called in the Republic.
Speaking on BBC Northern Ireland following the DUP party conference, Ms Foster said she hopes all sides will re-engage in talks to reach a solution and have devolved government reinstated.
She said she knew Brexit had been a "big shock" to the Republic but that politicians would have to "face the reality that Brexit will happen.
“Instead of megaphone diplomacy we should be engaging and finding a way forward.”
Ms Foster added that “consent” is a fundamental issue in the Belfast Agreement, but said the fact remained that Northern Ireland is an integral part of the United Kingdom.
“Every business I speak to does not want a border down the middle of the Irish Sea. The UK is our biggest market.”
The threat of an election remains despite talks on Saturday between Taoiseach Leo Varadkar and Fianna Fáil leader Micheál Martin, which ended without conclusion.
The pair met for an hour at a hotel in Dublin city centre to discuss the controversy over questions surrounding Tánaiste Frances Fitzgerald’s knowledge of the Garda strategy in relation to whistleblower Maurice McCabe at the O’Higgins commission.
In relation to Brexit, Mr Varadkar recently told British prime minister Theresa May the United Kingdom’s decision to “unilaterally” rule out important options in the Brexit talks has prompted Ireland and the EU to set their own non-negotiable red lines.
“What we want to take off the table, before we even talk about trade, is any idea that there would be a hard Border, a physical Border, or a Border resembling the past . . . Then we’d be happy to move on to phase two,” Mr Varadkar said.
Speaking at the DUP conference in Belfast, a number of MPs said an election in the Republic could help Brexit negotiations.
“I think it’s fantastic if there’s an election in the south because it will take Leo Varadkar’s attention away from Brexit, which is literally none of his business,” Ian Paisley jnr told PoliticsHome.
“He’s completely mishandled the arrangements and discussions . . . he’s adopted a policy of just yelling at the Border to make it an issue.”
Mr Paisley added: “Now that his mind might be focused on the election in his country that’s a good thing.”
Fellow MP Jim Shannon said: “I suppose it would distract from it in a way because all of a sudden he would be thinking about getting back in again.
“That might not be a bad thing from a point of view. I’m probably of the lobby who thinks an election would be good.”
Elsewhere, the Archbishop of Canterbury, Justin Welby has described Brexit as one of “the toughest, most difficult and urgent issues.”
He told ITV’s Peston on Sunday show that it was not just a question of trade and economics but of heart and identity.
“At its heart is the question of identity, of Ireland, Northern Ireland, the unionists, the nationalists in Northern Ireland, the whole of the rest of Ireland, saying who are we, and of the implicit deal that came in the Good Friday agreement about the questions of identity and the formation of identity, and that expresses itself in issues of trade and economics but is much more profound.”
The archbishop said Brexit is one of the major issues he has been discussing with the head of the Church of Ireland, the Archbishop of Armagh, whose diocese straddles the Border.
“He obviously doesn’t want to get to the point where he has to go through a checkpoint 30 times a day as he goes to and fro between parishes.
“I’ve been over there a lot, I meet a lot of people on both sides, right out to some really quite extreme people because the church meets all kinds of people, on both sides, and I think this is one of the toughest and most difficult and most urgent issues we’ve got to face.”
He added that he thinks it is going to take “quite a lot of imagination” to avoid a hard Border.
“I don’t personally know a way in which it can happen, but then I’m not . . . this is not my specialist area, you know I’m a clergyman, not a trade negotiator.”
The archbishop said he had been in favour of the United Kingdom remaining in the EU. “The only way we can face our challenges is as a united and reconciled country; what we can’t go on with is with the bitterness of the division among us.”
He said there needs to be much more discipline in the use of language, “the use of expressions about public enemies, the use of stuff like mutineers, all these headlines which seem conditioned to stir up hatred.
“There is a responsibility on anyone who is serving public opinion, to say yes, we disagree, we’re a democracy, of course we disagree robustly, sometimes very toughly, but we have to say we’re part of the same country and we will not surmount the challenge of Brexit or non-Brexit without you.”