First Minister Peter Robinson and the Deputy First Minister Martin McGuinness are to use the pre-arranged international meeting to discuss the A5 'roadblock' with the Taoiseach.
The 54-mile long carriageway would have slashed travel times from Northern Ireland to the Irish Republic.
Joint financial support to dual the road at a cost of £850m was established as part of the St Andrew's Agreement in 2006 and construction was expected to start in 2012.
The Stormont Executive has already expressed its disappointment at the decision by the Irish Government to withdraw funding from the A5 road scheme for the next budget period.
The DUP Leader Peter Robinson and Sinn Fein's Martin McGuinness were united on the issue after the news last week.
-- Advertisement --
The pair are again meeting the Taoiseach Enda Kenny after he travelled to Belfast on Thursday for a series of events and is now due in Armagh today.
They also had discussions with him on the issue at a Dublin meeting a week ago and now, the North South Ministerial Council will meet, hosted by the First Minister and Deputy First Ministers with the Irish Prime Minister Enda Kenny attending the plenary session.
Funding for the A5 road between Londonderry and Aughnacloy will be one of the key topics of discussion after the Irish reduced its funding for the project from £400m to £42m.
Mr Kenny said on Thursday night that he knew his government's "deferral of our funding contribution" to the project had "come as a big disappointment to many in Northern Ireland".
"But I want to stress - it is deferral, not abandonment," he added.
"My government remains fully committed to delivery of this important project, even if it must now be on a slower timeline."
Official Trip North
The Taoiseach was in Belfast on Thursday for several engagements - first, a courtesy call on the Stormont First and Deputy First Ministers - and then a visit to community projects on the loyalist Newtownards Road and the nationalist Short Strand to see some of the work being done on the ground.
He also visited Belfast City Hall and met the Sinn Fein Lord Mayor.
The Taoiseach then attended the Aisling Awards ceremony and dinner at the Europa Hotel as the guest of honour where he delivered the keynote address and presented the Person of the Year Award to Geraldine Finucane - widow of the murdered solicitor, Pat.
Enda Kenny's then pledged to lobby US politicians to push PM David Cameron to change his mind on the issue of a full inquiry into the killing after he refused one and instead ordered a review of the case papers by a leading QC.
(BMcC)
