With just four months to go before the deadline for a Brexit deal, he warned: "The hardest parts are still to do and there is not much time left to find a concrete agreement".
In a triumphant statement, Mark Daly, a member of a top Irish Parliamentary Committee, said "Brexit and the changing demographics of Northern Ireland" are going to end the province's United Kingdom membership.
The pair held a short meeting along with their delegations, including Clara Martinez-Alberola, head of Mr Juncker's cabinet, Gerard Kiely, head of the European Commission Representation in Ireland, legal adviser Michael Shotter and financial adviser Paulina Dejmek-Hack.
Earlier today, Barnier stated that the EU has advanced on "some separation issues" for which European businesses need certainty - such as customs, Value-Added Tax and certificates for goods.
"I am strongly against any temptation to try to isolate Ireland".
The future of the border between European Union member Ireland and Northern Ireland after Brexit is one of the most hotly contested issues in the negotiations, with many on both sides of the border wanting to keep the current free-flowing frontier open.
Mr Juncker was speaking in Dublin on Thursday.
Mr Juncker started his visit with a meeting with Taoiseach (Irish prime minister) Leo Varadkar and Irish Foreign Minister Simon Coveney at Government Buildings in Dublin.
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Referring to the UK's imminent departure from the EU, Mr Juncker told the Oireachtas that there is no deal as good as membership of the EU.
"The backstop paper has been amended and now expresses, in much more detail, the time limited nature of our proposal - something the prime minister and David Davis have always been committed to".
Juncker later told the country's parliament that the European Union has an "Ireland first" policy when it comes to Brexit negotiations.
Earlier this year, Mrs May rejected the EU's own proposed backstop solution to the Irish border issue.
The first vice-president will travel to Rotterdam this Friday (June 22) to address a conference entitled 'Countdown to Brexit: Are we ready?'. "It remains our intention to achieve a close economic partnership that does not require the backstop to be in operation".
"I would like to recall that the withdrawal agreement must contain a fully operational backstop solution for Ireland and Northern Ireland".
Taoiseach Leo Varadkar will attend the British-Irish Council summit in the Channel Islands later today.
European leaders meet in Brussels next week but a deal is not expected to be struck on the divorce's implications for the 300-mile border with its multiple crossing points until at least another European Council summit in the autumn.