The Northern Ireland Secretary has raised the possibility of calling Assembly elections if no power-sharing administration has been formed by January of next year.
Julian Smith discussed the deadlock at Stormont when he attended a meeting of the British Irish Council at Farmleigh House this afternoon.
He pointed out that the Westminster legislative provisions that allow power-sharing to be kept in cold storage run out on 13 January.
He said: "I want to focus on talks, I want to focus on getting [the] Executive back up and running, it is in Northern Ireland's best interests that we have the Good Friday institutions of the Executive and the Assembly functioning...but it is inevitable that if the piece of legislation comes to an end (on 13 January), there is a duty to call an election.
"I think that election would mark a failure of every politician in Northern Ireland and that's [why] I'm encouraging them as soon as this general election is over to sort out the outstanding issues and get back into power..."
The Taoiseach said what "we will need to do is let the elections play out in the United Kingdom, look at the results on the 13th or 14th December and then assess whether there is an opportunity to reconvene the talks and ask the parties to come together to get an Executive in place, ideally before Christmas but certainly before January 13th which is the next deadline".
Mr Varadkar was chairing a meeting of the British-Irish Council at Farmleigh this morning with Scotland's First Minister Nicola Sturgeon and Mr Smith among the participants.
The forum was set up as part of the Good Friday Agreement and Brexit featured prominently in the discussions.
The UK legislation Leo Varadkar and Julian Smith referred to is the Executive Formations and Exercise of Functions Act 2018. It allows Northern Ireland's Civil Servants to make decisions to protect public service and ensure good governance when there is no power-sharing administration in place.
Earlier this year as the stalemate at Stormont continued, the British government extended the use of the legislative instrument.
But as Mr Smith indicated today, he does not think it would be politically credible to further extend the cold storage arrangement if there is no breakthrough by 13 January.
Earlier, the Taoiseach said he does not think there is any form of Brexit that will be good for the Irish or British economies.
Mr Varadkar said that what has been achieved in the Withdrawal Agreement is "the protection of the common travel area and everything that flows from that".
He said there is also an assurance that there will not be a hard border between north and south, and that the all-island economy can continue to "develop and thrive" without any trade barriers between the north and south.
However, he said that the economic relationship that will exist between the UK and the EU - including Ireland - is still to play for.
"The outcome of those negotiations will determine the impact on our economies. If we do get to the point where the Withdrawal Agreement is ratified and the UK leaves the European Union by the end of January - and there's a lot of 'ifs' there - then the absolute priority has to be to move on to the next stage in negotiations."
Mr Varadkar said that from his point of view, the next stage is to ensure that we have a future relationship with the United Kingdom that "maintains the security cooperation that we have, political cooperation that we have, and cooperation in areas like education and research".
He said it is crucial for our economy that we continue to have tariff- and quota-free trade between Ireland and Britain.
Although next month's British General Election will temper engagement about Brexit, the participants at today's meeting discussed how the UK leaving the European Union might impact on relations between Ireland and the UK's regional administrations.
Ms Sturgeon is keen for the Scottish Nationalist Party to gain seats in the Westminster elections.
She has a Scottish independence referendum on her wish list and believes more heft in the House of Commons would help achieve that goal.
With no power-sharing administration in place at Stormont, Northern Ireland's executive was again unrepresented at today's gathering.