Several meetings are taking place in Dublin and Belfast
The Foreign Affairs Minister Charlie Flanagan says it looks like an election in Northern Ireland is now inevitable.
Mr Flanagan is holding a series of talks with political parties at Stormont today.
He is also meeting with the UK's Northern Ireland Secretary James Brokenshire, as efforts continue to resolve the row between the DUP and Sinn Féin.
Martin McGuinness resigned as deputy first minister on Monday, meaning an election is now likely.
Yesterday, the Taoiseach spoke to Mr McGuinness and DUP leader Arlene Foster by phone, and held a meeting with Gerry Adams and Mary Lou McDonald in Dublin.
Enda Kenny said: "A limited window for dialogue remains and I am encouraging the parties to engage together to find a way forward that delivers on the promise of the Good Friday Agreement and its institutions."
Meanwhile, the Social Democratic and Labour Party (SDLP) Leader Colum Eastwood is set to hold a series of meetings in Dublin.
In a statement, Mr Eastwood said the last 24 hours "have seen contradiction added to confusion".
He explained: "This morning I want to make clear that the SDLP is prepared to enter into negotiations with the Irish and British Government and the other parties. If a resolution to this mess is possible, the SDLP won't be found wanting in trying to find it.
"However, as other parties change their positions hourly, I want make reaffirm that the consistent SDLP position remains unchanged. If negotiations are to take place and a resolution is to be found, a full public inquiry and Arlene Foster’s removal is still the price the DUP must pay."
While Mr Flanagan predicts an extremely difficult challenge in putting together a Northern Ireland Executive after the public go to the polls.
"I say so in the context of the statutory binding legal position that the Secretary of State (James Brokenshire) on Monday, in my view, will be left with no choice but to dissolve the assembly and announce an election", he said.