Ian Paisley and other DUP ministers are attending a meeting of the North-South Ministerial Council for the first time.
The meeting, in Armagh, includes members of the executive and Taioseach Bertie Ahern and other Irish ministers.
The council first met in 1999, but was spurned by the DUP. Mr Paisley said they were entering "new territory".
"We are meeting under a new aegis because of the alterations made during the negotiations to get this new government off the ground," he said.
"This is new territory to a large extent and I hope it will be very successful."
Taoiseach Bertie Ahern said developments in Northern Ireland recently had been "extraordinary".
"What's happened since 8 May has been extraordinary and very successful and I very much acknowledge what the first minister and the deputy first minister have done these last two and a half months."
DUP ministers had boycotted the council - set up under the Good Friday Agreement to increase cross-border cooperation - branding it "unaccountable" and "an embryonic united Ireland".
Speaking as he arrived in Armagh on Tuesday, the Northern Ireland first minister said he viewed the body as one in which "there is no competition between the two sides in the body".
"We have one issue - we want both parts of Ireland to prosper," Mr Paisley said.
Mr Paisley was accompanied by Deputy First Minister Martin McGuinness, who said the meeting was "another mighty leap foward".
"There is clearly in our own vested interests the need to ensure the success of all of these institutions - and we are going to work to ensure that they are successful," he said.
Discussion is expected to focus on transport issues including the upgrading of the main road from Omagh towards Donegal and the restoration of the Ulster Canal between Clones and Upper Lough Erne.