Enda Kenny is planning an all-island forum following the decision by the UK to leave the European Union.
Enda Kenny is meeting with his Northern Ireland counterparts today, for the first time since the UK referendum result to leave the EU.
First Minister Arlene Foster and Deputy First Minister Martin McGuinness have brought their ministers to Dublin for a North South Ministerial Council meeting.
There was already a busy agenda for the joint meeting between ministers from Dublin and Stormont - but the fallout from the Brexit vote will cast a long shadow over the gathering.
The meeting illustrates some of the Taoiseach's challenges in containing the fallout.
Ireland can only plan to a certain degree, because no talks can begin until a new prime minister is elected in Westminster.
While both Foster and McGuinness are keen for the border to remain open, they stood on different sides of the Brexit debate - and have differing attitudes about what should happen next.
Speaking in Dublin this morning, Mr McGuinness suggested it would be disastrous for the six counties to be forced to leave the EU.
"We can't afford to be in chaos, we can't afford to be in turmoil," he said.
Speaking ahead of the Council meeting, Enda Kenny said: "This plenary meeting will provide an opportunity for us to have a strategic and constructive discussion on the impact of the referendum for Northern Ireland and the all island implications of the vote, and how we are going to work together to protect the interests of all our citizens on the island of Ireland."
It was confirmed over the weekend that the Taoiseach is planning an all-island forum following the UK's referendum, and the idea is expected to be on today's agenda.
The proposed forum was welcomed by Sinn Féin leader Gerry Adams, who suggested: "There is an imperative on all of those who are concerned about the consequences of the Brexit vote to work together in the time ahead."
The North's health minister, Sinn Féin MLA Michelle O'Neill, hopes Northern Ireland could remain a part of the EU, despite the Brexit result.
She told Newstalk Breakfast that they need to see the shape of what the all-island forum will look like.
"Very clearly for us, that forum needs to be very representative of those people that voted to stay and those people that voted to leave," she added.
Today's meeting in Dublin comes as British Chancellor George Osborne announced plans to cut corporation tax to less than 15%.
He said Britain must show the world it is "still open for business" as he outlined plans to build a "super competitive economy" with low business taxes and a global focus.