Taoiseach Enda Kenny and his ministers will embark on a series of trade missions in the coming months as they actively seek to attract post-Brexit business.
After next Monday's meeting with British Prime Minister Theresa May, Mr Kenny will begin planning trips to Malta, Poland, the United States and Germany.
He has also said every minister who signs up to travel abroad for St Patrick's Day will be ordered to schedule meetings with companies who have links to Ireland or could potentially invest here.
"Brexit is the number one priority for the foreseeable future," the Taoiseach said. "This is the single most important issue economically of the last 50 years. In advance of the triggering of Article 50, we have been intensifying our own preparations and our international engagement."
He said the Government was considering the requirements for extra trading capacity within the eurozone and beyond, adding that Canadian businesspeople had expressed "a lot of interest" in Ireland.
"And for those who will be travelling abroad for St Patrick's week, there will be a specific trade element built in to all of there visits.
"It's not just going to participate in some occasion around St Patrick's Day, it's going to be meeting with companies who are exporting from Ireland and ones who might create new investment," he said.
Mr Kenny said he looked forward to welcoming Mrs May to Dublin on Monday.
"We've got quite a deal of issues to discuss about the Border, the common travel area, our trading links, our place in the European Union and how we maintain links as close to what they are," he said.
The Taoiseach has refused to appoint a Brexit minister on the grounds that he is leading the Government response.
"I chair the Cabinet committee on Brexit, all ministers are involved in this. I've asked them to prepare papers in respect of their responsibilities.
"I call ministers in as necessary so that we can get an entire government response on a constant basis.
"This is far too serious to leave to just one minister," he said.
Asked about how long he intends to remain in office, Mr Kenny replied: "I am focused on the agenda of Government here.
"A big Programme for Government, 600 commitments, a whole range of activities.
"We are not going to be fazed here by Brexit and international relations.
I don't expect there will be any alteration from what we have with the Fianna Fáil party in terms of the supply and confidence [deal] and the review at 2018.
"There is a very big agenda here. We are not going to be diverted by extraneous matters."