Taoiseach Leo Varadkar has said there is a "real risk" an October deadline for a solution on the Irish border could be missed if "real and meaningful progress" is not made by next month.
It comes as pressure mounts on the UK's chief Brexit negotiator David Davis to clarify his country's vision for the border on the island of Ireland after Britain leaves the European Union in March 2019.
Speaking during Leader's Questions in the Dail on Wednesday, Mr Varadkar said a lack of progress by the UK on a withdrawal agreement by the time the European Council meet in June could put the October deadline - in place to allow UK and European parliaments time to ratify any such agreement - in jeaprody.
"It’s still early May, it’s the first week of May," Taoiseach Varadkar added.
"There are a lot of moving parts. There are shifting sands, there is an important UK Cabinet meeting underway today [Wednesday], and there are parliamentary votes of significance happening now."
On Tuesday David Davis was been called on by the Northern Ireland Affairs Committee to explain his vision of a post-Brexit border on the island of Ireland.
Chair of the Committee Dr Andrew Murrison MP said he was repeating an invitation first made in March, and that "to date, we have not seen a worked up, coherent proposals that would allow the UK to be freed from the structures of the Customs Union and Single Market and avoid additional infrastructure at the border".
Conservative MP Murrison says the letter is a "genuine and sincere opportunity to rectify this".
On Monday and Tuesday the EU's chief Brexit negotiator Michel Barnier made a visit to Northern Ireland and the Republic, making stops in Dungannon, Newry, and Londonderry.
Writing in the Belfast Telegraph, Mr Barnier said he was looking for "practical solutions to avoid a hard border" and his priorities in such a deal were protecting the Good Friday Agreement, ensuring north-south cooperation (including on economic matters), and respecting the UK's constitutional order.