Irish foreign affairs minister Simon Coveney says his government's relationship with the DUP needs to be repaired.
Coveney blamed tensions around agreeing phase one of the Brexit deal.
He said he wanted to meet DUP representatives before the end of the year.
In an interview with RTE, Mr Coveney said, "Because of the tension around trying to get the deal we felt was needed for everyone on this island, yes, of course there is repair work to do."
The DUP has accused Irish premier Leo Varadkar of "politicking" over Brexit.
The Taoiseach has said Brexiteers need to acknowledge that they created the difficulties surrounding the Northern Ireland border.
A compromise agreed between the EU and UK has been the subject of a range of interpretations.
Mr Varadkar has said he is confident there will be no hard border on Ireland despite being warned the issue remains a "riddle to be solved".
The DUP's 10 pro-Brexit MPs are supporting Theresa May's minority Government in crucial votes.
The unionist party scuppered earlier British Government efforts to agree a border deal with the EU.
The problem centred on whether Northern Ireland continued to follow some of the rules of the EU's single market after the separation and the DUP was keen to ensure there would be no divergence from the rest of the UK.
Mr Coveney said the absence of a power-sharing ministerial Executive at Stormont was part of the problem of Brexit.
If Sinn Féin and the DUP cannot agree to resurrect the Executive, Mr Coveney said the Good Friday Agreement needed to be looked back at, because that was where the rules were set.
He added, "Then there is the prospect of a whole series of other choices - from another election, to the triggering of Intergovernmental Conferences to make decisions on Northern Ireland."
"That is not where we want to be. That will cause tension. It will be a very frosty environment to make decisions in... so we all have a responsibility, in a practical sense, to find a way forward."