Taoiseach Leo Varadkar has said there would be a great deal of reluctance among European Union leaders to grant Britain another extension to negotiations to leave the bloc if a new prime minister sought one.
"I certainly wouldn't rule it out and from Ireland's point of view, we would be as facilitative to the UK as is possible but I think a lot of other countries have become very frustrated at these rolling extensions," Mr Varadkar said.
"So if there was an extension, it would have to be for a particular purpose, not for renegotiations, not for indicative votes (in the British parliament) but in the context perhaps, if there were to be a general election in the UK or something like that but we are getting ahead of ourselves there."
Earlier, Tánaiste and Minister for Foreign Affairs Simon Coveney warned that the chances of a disorderly Brexit have never been higher and the Government now considered the risk of this outcome on 31 October as significant.
Mr Coveney will bring to Cabinet tomorrow a detailed update on contingency planning for a no-deal Brexit with this possibility now just 115 days away.
The Government's updated plan to deal with a hard Brexit will be published this week and it will also be debated in the Dáil.
The plan will build on the major piece of legislation passed by the Oireachtas in March and it will outline what supports are available to those needing to step up preparations.
Writing this morning in The Irish Times, the Tánaiste said there have been inaccurate comments in recent weeks about the Irish Government, the EU and the backstop.
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In what appears to be a clear reference to the Tory party leadership campaign, Mr Coveney said people can have their own opinions but they cannot have their own facts.
He reiterated that the backstop is essential to protect stability on this island.
Those who claim Northern Ireland would not hurt too badly in a no-deal scenario should listen to the bleak reports of Northern Ireland's civil service and also heed the warnings of business groups, Mr Coveney states.
He added that no-deal planning work with the European Commission will continue in the weeks ahead where there is a shared twin objective to prevent a hard border while also protecting the EU's single market.
The Tánaiste said Ireland's number one contingency is and will remain the country's EU membership with the support and security it brings.