The idea of appointing a 'Brexit Minister' has been firmly ruled out by Taoiseach Enda Kenny, who said he wants to oversee the Republic's strategy himself.
Irish business leaders and Opposition parties have called on the government to create a new ministry to deal specifically with the threat posed by Brexit, but Mr Kenny said: "We cannot give this any higher political status than the office of the Taoiseach.
"Every single minister is a Brexit minister, as is every minister of state."
Mr Kenny argued that if he appointed a junior minister to the role he would be accused of "downgrading" its significance, and if he appointed a Cabinet minister people would say: "You need to take a greater interest in this yourself".
"I accept that I'm very busy and Brexit is going to take up a lot of time for everybody over the next period, but I've no qualms at all about saying this should be vested in the office of the Taoiseach and that's why I intend to lead it," he said.
The Irish government has set up a Cabinet sub-committee dedicated to the Brexit response.
"It's very important that you understand that the coordination impact of the office of the Taoiseach is far stronger, with respect to every department," Mr Kenny said.
"I chair these meetings and will continue to chair them, and call ministers as needs be.
"All of them are under a mandate to talk to their counterparts in Europe to explain the different circumstances here."
Mr Kenny noted that the Council of European Leaders will be making the key decision in relation to Brexit negotiations with the EU.
He also revealed that a meeting of the 27 member states who will remain inside the EU is to be held in December, with British Prime Minister Theresa May excluded.
"So this is far too serious a matter to have it hived off, either to a section of a department, or to a minister who has responsibilities in other places.
"I want to make that clear that this is a whole-of-government response.
"Everybody who has connections, either with Northern Ireland, the United Kingdom or Europe, can play their part in that. These preparations are going to intensify over the next few weeks," Mr Kenny told a briefing of reporters.
Mr Kenny said next week's Civic Forum on Brexit will be attended by over 300 people, including political and business leaders.
It will be the first in a series of meetings that will include sectoral gathering around the country and in Northern Ireland.
Mr Kenny is also to travel to the east and west coasts of the United States next month on a trade mission.
He will meet with financial houses and business leaders to ensure there is an awareness that Ireland will continue to be a member of the EU after the UK leaves .
"I expect that we will continue to be a very attractive location for investment," Mr Kenny said.