The new DUP leader, Edwin Poots, is to meet the Taoiseach in Dublin on Thursday evening.
It will be Mr Poots’ first visit to Dublin to meet Micheál Martin since he was appointed as DUP leader.
They are expected to discuss the Northern Ireland protocol and North-South relations.
Mr Poots has been highly critical of the relationship between Belfast and Dublin, which he claimed in the Assembly last month had "never been worse."
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He blamed "the Republic of Ireland led by Mr [Leo] Varadkar and Mr [Simon] Coveney in particular" who he said had "sought to create barriers between Northern Ireland and Great Britain, our main trading partner."
However speaking on BBC Radio Ulster's Good Morning Ulster on Thursday, the DUP MLA Paul Givan – who is regarded as the most likely to be the North's next First Minister – said the North-South relationship was a "very important one" and that "of course we want to have good relationships with our closest neighbour."
He also emphasised that the Northern Ireland protocol “has caused huge damage with no consent from the unionist people or its representatives and that has had a very negative influence in terms of those relationships, and that’s something that we all collectively need to address.”
He said Mr Poots was due to travel to Dublin to meet the Taoiseach on Thursday evening and added: “I know that Edwin [Poots] wants to be able to address these issues with the Taoiseach, and I think he’ll have more to say about the whole North-South dynamic later today.
“It is vitally important that people understand, in the Republic of Ireland, the challenges and difficulties that unionism faces, but we do need to identify and navigate a way through these difficulties,” he said.
North-South meetings
On Wednesday night the North's Minister for Communities, Deirdre Hargey of Sinn Féin, said she was seeking legal advice on bringing a judicial review against DUP ministers who refuse to attend North-South meetings, saying their advice may be in breach of the ministerial code.
On Wednesday a North-South ministerial meeting on language issues could not go ahead after the DUP junior minister, Gordon Lyons, failed to attend.
The DUP has boycotted a number of cross-Border meetings in recent months as part of its campaign against the Northern Ireland protocol.
Mr Poots and the other leaders of the five parties in the Northern Executive are to take part in a meeting of the Party Leaders’ Forum later today amid concerns that uncertainty around the nomination of a new DUP first minister and changes to the ministerial lineup – which are yet to be announced by Mr Poots – are creating political tensions and could potentially spark a crisis which could threaten the stability of the power-sharing institutions.
There has been speculation that Sinn Féin could seek to use the process to secure assurances from the DUP around sticking points such as the implementation of Irish-language legislation.
It has been reported that Arlene Foster could remain as First Minister until after a meeting of the British-Irish Council in her home county of Fermanagh next week.
Mr Givan on Thursday would not be drawn on whether he would become the next First Minister, saying “that’s a matter for Edwin” but indicated that if he was asked to take on the role he would do so.
“In due time he’ll make his announcements in respect of that, he has had conversations with all of us but he’s finalising that decision-making process so I would anticipate we’ll not have too long to wait to find out what his plans are,” he said.
“I haven’t asked for anything and I haven’t been asked to do anything at this stage, what I have made clear to Edwin is if he sees me having a role to be able to serve the party and to serve the country I’ve never shirked away from taking on that responsibility.”
