European Union leaders have said they want to avoid a hard border on the island of Ireland as part of its Brexit negotiating guidelines with the UK.
The 27 EU leaders unanimously agreed on Saturday the guidelines issued in March by European Council President Donald Tusk.
In a letter to the leaders of the EU-27 ahead of the summit, Mr Tusk wrote that progress on "people, money and Ireland" must come before negotiations on the EU's future relationship with the UK.
Taoiseach (Irish prime minister) Enda Kenny hailed the outcome of the summit in Brussels as "a huge endorsement of the government's approach to the Brexit negotiations and a clear recognition of the unique and specific challenges facing Ireland".
Mr Kenny said the declaration on Irish unity, in which the EU affirmed that in the event of a successful referendum on a united Ireland, Northern Ireland would automatically rejoin the EU, was hugely important.
"It is important to provide reassurance that it does not undermine any provision in the Good Friday Agreement, and if the provision on unity by peaceful means and by consent and democratic means is invoked at some time in future, EU membership is assured, and is now unanimously accepted by the European Council to endorse that legal base," he said.
"Let me be clear, this is not about triggering any mechanism. I've been very consistent in my view that the conditions for a referendum do not currently exist. But an acknowledgement of the principle of the potential within the Good Friday Agreement is hugely important."
The UK's Brexit Secretary David Davis had previously said that in the event of such a vote, Northern Ireland could become "part of an existing EU member state".
Sinn Féin's Mary Lou McDonald said EU leaders were helping to create a united Ireland.
"We welcome the fact that European leaders have recognised the provision within Good Friday (agreement) to end partition and to create a united Ireland," she said.
"We welcome the fact that a reunified Ireland would in its entirety automatically fall within the European Union.
"We think that that is logical and fair and we welcome the fact that European leaders have said that now out loud."
Talks with the UK will begin after the general election on 8 June. The deadline for completing the negotiations is 29 March 2019.
Former First Minister Lord Trimble said the issue of tariffs would be important in whether or not there would be a hard border after Brexit and said there may need to be a change in EU law.
"If there are tariffs and under existing EU law a member state who has part of the EU's external border has to put in place on that border appropriate installations to enable them to monitor the movement of that border," he said.
"If on the basis of where we're going, if there are tariffs, then it becomes a hardish border and it comes so by virtue of EU law."
The separation talks will seek to agree the rights of EU citizens living in the UK, as well as Britons living in the EU, plus a settlement for the UK's financial obligations as an EU member state. A deal must also be agreed to avoid a hard border between the Republic of Ireland and Northern Ireland, Mr Tusk wrote.
However, the UK government has said made clear that it want talks on trade relations to run in parallel with the separation negotiations.
EU officials estimate that the UK faces a bill of €60bn (£51bn; $65bn) because of EU budget rules. UK politicians have said the government will not pay a sum of that size.