Leo Varadkar and Theresa May have said it is still possible to revive powersharing in Northern Ireland.
The two leaders spoke on the phone about the latest twist in the political deadlock at Stormont as the UK Prime Minister's government makes preparations to impose a budget on the region by the end of the month.
In a statement from the Taoiseach's office while he is on a trade mission to the US west coast, the leaders said the gap between the two sides is narrow.
"Both leaders also expressed the view that it is still possible to form an executive which would be in the interests of all the people of Northern Ireland," an Irish Government spokesman said.
Mr Varadkar told Mrs May there could be no return to direct rule like it was before the 1998 Good Friday Agreement.
Have spoken with PM May re Northern Ireland. We both agreed it's still possible to form an Executive. Provisions of GFA must be honoured.— Leo Varadkar (@LeoVaradkar) November 2, 2017
The Taoiseach's office said Mrs May made it clear she did not want to see a return to Westminster running all of Northern Ireland's affairs and that budget preparations were not the first step on that road.
"Both leaders agreed that there is still time to reach an agreement," Mr Varadkar's office said.
Northern Ireland Secretary of State James Brokenshire is to outline the state of powersharing talks when he addresses the House of Commons.
The DUP and Sinn Fein failed to meet Mr Brokenshire's original Monday deadline for a deal, after Stormont had been effectively in limbo since January.
Irish language rights and other cultural issues are the main sticking points.
Despite the deadlock Mrs May is understood to remain committed to a £1 billion investment in Northern Ireland agreed as part of a voting pact between the Conservatives and the DUP at Westminster.
Meanwhile, Fianna Fáil's Brexit deputy has said a Northern Executive is vital to help prepare for Brexit.
Deputy Stephen Donnelly said a Westminster Budget will not have the vision to prepare Northern Ireland for what lies ahead.
He has joined others in calling on Sinn Fein and the DUP to find a way to end the current political impasse.
"Brexit is, without a doubt, the biggest economic threat to Northern Ireland since The Troubles and it is completely devoid of political leadership," he said.
"It beggars belief that the parties involved have essentially refused to find a compromise whereby they can put the Assembly together and put political direction in place so that the people of Northern Ireland know how they are meant to face the challenges that Brexit poses."