Tánaiste and Minister for Foreign Affairs Simon Coveney has said the heat needs to be taken out of the discussions around fishing in Rockall and the less that is spoken about boardings and potential clashes the better.
Speaking in Cork, Mr Coveney said Ireland's position is very clear - Ireland has been fishing there for many years and there has never been an enforcement issue.
The Scottish government said last week that it will take action against Irish vessels it says are fishing illegally around Rockall, which lies around 230 nautical miles northwest of Donegal and 240 miles west of Scotland in the North Atlantic.
Mr Coveney said he recognised there is a very different legal view in the UK and Scotland, but the way to resolve these issues is not to force Ireland to change its policy towards Rockall - and its legal opinion in relation to Rockall - by a threat of enforcement.
He said there are diplomatic channels "very much open at a very senior level in both governments today" and this is the way to resolve these issues, through negotiation and discussion.
He said what he does not accept is that a very small rock constitutes a sovereign territory that can have a 12-mile fishing limit set around it.
This, he said, is what the Scottish government is claiming and that interpretation is not accepted by the Irish Government and why Irish boats are legitimately fishing in and around Rockall.
Mr Coveney said these are EU fishery grounds and the Common Fishery Policy applies.
"Scotland and Ireland are very close friends and we will work with them to try and bring an end to this, but what we won't do is change a policy which we have had in place for decades on the back of a threat."
The Chief Executive of the Irish Fish Producers' Organisation, Francis O'Donnell, said Rockall is critically important for Irish fishermen, particularly from the ports of Killbegs and Greencastle.
He told RTÉ’s 6.1 News that for some fishing vessels, their catch from the area would account for up to 30% a year.
Mr O’Donnell said that over the last two years, there has been a slow build up to the current situation and there has been significant correspondence between the Scottish and Irish governments.
He said Ireland has always fished at Rockall and are issued a quota annually by the EU to fish there.
He said the Scottish National Party wants to remain in the EU whereas Scottish fishermen want to leave, and he believes there is a political motivation behind the latest move.
Sinn Féin's finance spokesperson Pearse Doherty described the Rockall situation as "bizarre".
Speaking on RTÉ’s News at One, the Donegal TD said Scottish authorities have signed up to the common fisheries policy, which allows for Irish vessels to fish in that area.
Mr Doherty said it has always been that way and there is never been an issue before.
"I'm bewildered by the fact that these negotiations were going on for quite a period of time without the knowledge of other Oireachtas members. The fishing community themselves only learned about this on Friday.
"It's bizarre that this wasn't raised at the most senior level between the Taoiseach and Nicola Sturgeon when they met last month."
He said the issue now needs to be resolved and that intense negotiation is needed between senior politicians here and their counterparts in Scotland.
Mr Doherty said Irish fishermen who are carrying out their duties legally and in compliance with the common fisheries policy must be protected.
He said a situation where Scottish authorities board Irish vessels could not be allowed.
Earlier, the CEO of the Scottish White Fish Producers Association said Irish trawlers have been fishing illegally in Rockall for a number of years.
Mike Park said that UNCLOS (law of the sea) states that Scotland is well within its rights to manage a 12-mile territorial limit.
Speaking on RTÉ's Morning Ireland, he said it is just a small area of Rockall that Irish trawlers are banned from.
Mr Park said Scotland has a right to impose restrictions and is not being overly zealous about it.
He added that the Irish Government has been warned for a number of years about this issue but "for whatever reason" has ignored it and it has come to the point where the Scottish government has said "no more".
Mr Park said he did not believe the disagreement is a big deal at all but that fishermen in a modern era must abide by the law.
He added that he did not believe the issue was directly related to Brexit and that the problem went back a number of years.
He said he had a great deal of sympathy with Irish fishermen but that at the end of the day they must abide by the law the same as everyone else.
Minister for Agriculture and the Marine Michael Creed said yesterday that Ireland had a right to fish in the area under EU Common fisheries law and the Government would exhaust all legal options in the context of defending the interests of the State and Ireland’s fishing industry.
The captain of one of the Irish vessels fishing around Rockall said he would refuse to leave and the news of the Scottish warning came as a complete shock.
Adrian McCleneghan, captain of the Northern Celt, said he has been fishing in the area for the past 15 to 20 years and has been boarded on numerous occasions by the Scottish navy, but it was never an issue before.
He said both Scottish and Irish fisheries patrols have carried out routine inspections of his vessel over the years without issue and if he was now asked to leave he would refuse.
Speaking on the same programme, Mr McCleneghan said: "I feel we have a right to fish here. I don't feel the Scottish fisheries patrol or the Scottish government can ask us to leave so I would refuse to leave."
He said one or two Irish vessels have left the area because they do not want to get caught up in legal cases if their vessels were detained.
Mr McCleneghan said: "We've been told by the minister that the Irish vessels have a right to fish here and to continue fishing and we would have full backing financially and legally from the government if one of the boats is detained here, so hopefully they come to a resolution on the situation."