TAOISEACH Enda Kenny said he and British Prime Minister Theresa May are in agreement that there will be no return to direct rule in Northern Ireland.
Addressing a business event in New York, Mr Kenny urged the parties at Stormont to focus on forming a new powersharing executive.
Following a snap election at the start of the month, politicians next week will enter a third and final week of negotiations to strike a deal before a statutory deadline.
If the deadline passes without an accord to bring together a new powersharing executive involving the two main parties - Sinn Fein and the DUP - the UK government is legally obliged to call another election.
Some have predicted that, in those circumstances, the UK government might move to pass emergency legislation to reintroduce Westminster direct rule in Northern Ireland.
Mr Kenny's remarks at Bloomberg's offices in New York suggested that Mrs May has ruled that option out.
"I hope that the elected members of the Assembly will now focus through their parties on actually putting an executive in place within the three weeks from the date of the election," he said.
"If that doesn't happen the Secretary of State for Northern Ireland (James Brokenshire) would then either have to hold further elections or have direct rule again from Britain.
"I have spoken very clearly to the British Prime Minister and we are both agreed that there will be no return to direct rule from London.
"So I do hope that the executive can be put in place, because this has implications for the peace process."
During the event, Mr Kenny also said Ireland will not be following the UK out of the EU.
"To continue to succeed as an open economy and welcoming society, we must and we will remain at the very heart of Europe," he said.
In terms of Brexit, he said: "It is not a trigger for Ireland to follow suit and leave the European Union with the United Kingdom - we will not do so."
His comments came just hours after he indicated he will not announce any retirement plans until political uncertainty in Northern Ireland is addressed and the EU's negotiating stance on Brexit is agreed.
Mr Kenny said those "immediate priorities" would take precedence over "everything else" on his return to Ireland.
Mr Kenny, who has been Taoiseach since 2011, had been under pressure to set a timetable for his departure following criticism of his handling of a number of recent political controversies in the Republic.
After taking part in the St Patrick's Day parade in New York, he made clear that dealing with his own future would take a back seat to pressing concerns at Stormont and within the EU.
"What I did say to my own party was I would deal with this matter effectively and conclusively, and that is my intention, but I think these are priorities that take precedence over everything else," he said.
"You can't have a situation where you have no leadership in Northern Ireland and where we have to define from a European Union point of view where Ireland would be, what the agreed terms of reference for the (Brexit) negotiations are."