The Taoiseach has said it will be practically and legally "extremely difficult" to find ways to maintain an open border with Northern Ireland after Brexit, even with the sympathy and goodwill of the European Union.
The border is set to be the only land frontier between the United Kingdom and the EU once Britain leaves the bloc in early 2019.
British Prime Minister Theresa May has said she wants the border to be as seamless as possible, and EU negotiating guidelines call for the avoidance of a "hard border".
But with the exact nature of Britain's future ties with the bloc unclear, solutions to the border issue have yet to be proposed.
"From my meetings in Brussels and elsewhere, there is a real understanding of the issues that are unique to Ireland, a sympathy for us and a lot of goodwill," Leo Varadkar told the National Economic Dialogue at Dublin Castle this morning.
"But turning those into practical solutions that will be written in law is going to be extremely difficult... The Irish issues, including avoiding an economic border, will not be easy to solve."
Mr Varadkar maintained his predecessor Enda Kenny's view that Ireland would ask the EU for specific assistance in dealing with the economic fallout from Brexit.
Ireland's top civil servant overseeing Brexit planning said last month that one of the areas being examined was a potential exemption from EU state aid rules, enabling Ireland to provide financial support to companies adversely affected by Brexit.
Ireland's export-focused economy has close trade links with its nearest neighbour, particularly among smaller firms that do little trading further afield, and businesses fear Brexit will lead to a costly rise in tariffs, paperwork and transit times.
"The level of uncertainty as to the outcome of the negotiations remains very high, and it's clear that Brexit is a fundamental economic risk for Ireland if it results in a permanent change to the rules of trade between our two countries," Mr Varadkar said.
"We will make a strong case at the EU level that Ireland will require support that recognises Brexit as a serious disturbance to our economy, once we've a better understanding of what that disturbance is going to be."