The UK has delivered its "road map" for implementing the Northern Ireland Protocol to the EU.
Lord Frost, the UK's lead Brexit Minister, and EU Commission Vice-President Maroš Šefčovič spoke on Wednesday.
The protocol is the part of the Brexit withdrawal deal that created the Irish Sea border.
Earlier this month, the UK government changed how the protocol was being implemented without EU agreement.
It delayed the introduction of new sea border checks on food, parcels and pets.
It also moved unilaterally to ease the trade in horticultural products across from Great Britain to Northern Ireland.
The EU has begun legal action as a consequence.
'No checks on the island'
Last week, the EU said it expected the UK to deliver a document, which the UK has referred to as an "agreed work programme", following a meeting of senior officials who are overseeing the Northern Ireland deal.
Earlier this evening, the EU's former Brexit negotiator, Michel Barnier, said it is "of the utmost importance that it (the withdrawal agreement) is thoroughly applied".
He added that this included "putting in place the necessary checks between Great Britain and Northern Ireland".
Mr Barnier, who was delivering a speech on his final day of working at the European Commission, said that all sides "agree that there can be no checks across the island of Ireland".
However, the Northern Ireland Protocol has been opposed by Northern Ireland's unionist parties who have said it undermines their place in the UK.
Under the terms of the Brexit withdrawal treaty, the protocol can only be removed by a majority vote of the Stormont Assembly, with a vote due in 2024.
Lord Frost has previously said it is difficult to see how the protocol can be "genuinely durable" without the consent of "all of the people" of Northern Ireland.
Earlier on Wednesday, the Irish Foreign Minister, Simon Coveney, said he had become "somewhat of a bogeyman" by trying to tell the truth about the protocol.
He said the irony was that his office has been telling Brussels about the need to understand the tensions in Northern Ireland.
Mr Coveney said it was not just about Northern Ireland, but about the island as a whole.
He said dismantling the protocol would mean infrastructure on the border, which would not be accepted politically.
"We would be taken out of the single market by default," said the minister.
"The protocol is not just about Northern Ireland; it is about the island as a whole functioning as it needs to function in order to protect relationships and trade."
He said it was designed as much in London as it was in Brussels, "but many people seem to conveniently forget that".
The protocol was not going to be cast aside, but efforts would be made to address "genuine concerns", Mr Coveney told the Seanad, Ireland's upper house, earlier this week.
Graffiti singling out both Tanáiste (Deputy Prime Minister) Leo Varadkar and Mr Coveney have recently appeared on walls in parts of Belfast..
Mr Coveney said easing the trade burden must be done through cooperation and partnership.
"We cannot have a situation where one side, whether it be the EU or the UK, decides unilaterally to declare that it is going to implement the protocol in one way or another, in a manner that contravenes not only the spirit of the protocol but the legal obligation under the protocol as well."
The minister said the Republic of Ireland had also suffered trade disruption as a result of Brexit.