The Taoiseach Leo Varadkar says Ireland wants a UK commitment to no border on the island of Ireland 'in writing'.
He has met British Prime Minister Theresa May on the sidelines of an EU summit in Sweden.
Mr Varadkar is in Gothenburg, where he is attending the EU Social Summit for Fair Jobs and Growth.
He met Mrs May ahead of the summit to discuss Northern Ireland and Brexit.
The Government says Mr Varadkar emphasised the importance of upholding all aspects of the Good Friday Agreement including the power sharing institutions, and continued to urge the Northern Ireland parties to reach agreement.
Bilateral meeting with Theresa May before EU Social Summit, discussing Northern Ireland and Brexit pic.twitter.com/H2hQZvniJa
— Leo Varadkar (@campaignforleo) November 17, 2017
This meeting comes in advance of December's meeting of the European Council - where a decision will be taken on whether or not to progress to the next phase of Brexit talks.
Speaking after the bilateral meeting, Mr Varadkar said: "We've been talking 18 months, we've been given assurances now for 18 months since the referendum that there'll be no hard border in Ireland, that there won't be any physical infrastructure, that we won't go back to the borders of the past.
"We want that written down in practical terms in the conclusions of phase one."
He denied that Ireland was pushing for Northern Ireland to remain in the EU Customs Union while the rest of the UK remained outside.
"It's not saying that, and I don't think it is hugely divergent from the UK position that they would like to enter a customs partnership with the EU after Brexit.
"What we want to do is set the parameters for the talks about trade."
He noted that it was the British Government that took the option of remaining in the customs union and the single market "off the table" before talks on trade could begin:
"What we want to take off the table before we even talk about trade is any idea that there would be a hard border, physical border or border resembling the past in Ireland.
"So once those parameters are set, then we'd be happy to move on to phase two - provided the other issues of course are resolved as well".
The summit will be followed by a working lunch for leaders chaired by President Donald Tusk.
This is the first in a series of discussions under his agenda, as endorsed by the October European Council, and will focus on education and culture.
Meanwhile Foreign Affairs Minister Simon Coveney has hosted the British Foreign Secretary Boris Johnson in Dublin on Friday.
They held official talks at Iveagh House, with Brexit again topping the agenda.
Boris Johnson says the issue of the border will be dealt with at next stage of Brexit negotiations, and we should move there now.
Simon Coveney slaps that down and says we’re not ready to move on next pic.twitter.com/qs2AHI5eEW
— Sean Defoe (@SeanDefoe) November 17, 2017