The Irish government has said Brexit trade deal talks should not proceed until there is a firm commitment to preventing a "hard" Irish border.
Taoiseach (Irish Prime Minister) Leo Varadkar said the assurance must be written down before the talks move on.
"Before we move to phase two talks on trade, we want taken off the table any suggestion that there will be a physical border," Mr Varadkar said.
He was speaking at a European summit, attended by Prime Minister Theresa May.
'Chained to the EU'
Mrs May's spokesperson said both leaders had agreed to work together to find solutions ensuring there is "no return to the borders of the past".
But Sammy Wilson from the Democratic Unionist Party (DUP) accused the Irish government of trying to "keep the UK chained to the EU".
Earlier, Mr Varadkar's message was echoed by Irish Foreign Minister Simon Coveney, who held talks with his UK counterpart, Boris Johnson, in Dublin.
Mr Coveney said there was "a sense of jumping into the dark" for Ireland, as the future operation of its border with Northern Ireland had not been agreed.
"Yes, we all want to move onto phase two of the Brexit negotiations, but we are not in a place right now that allows us to do that," the foreign minister said.
The UK is due to leave the EU in March 2019, but Mr Coveney suggested the exit process could take up to five years.
"Deal or no deal'
In response, DUP MP Sammy Wilson claimed the Irish government was "fully signed up with the European establishment to thwart the referendum result in the UK to leave the EU."
In a statement, the MP accused Irish ministers of "trying to block the UK moving on to substantive negotiations about leaving the EU, and then suggesting that an interim or transitional period of five years is going to be needed before we can leave".
"The objective is quite clear; keep the UK chained to the EU until after the next election, when the Irish government hope that Corbyn's Brexit-breaking MPs might be in power," Mr Wilson added.
He said it seemed like the Irish government were content to involve themselves in the affairs of another state.
The MP for East Antrim said that the DUP will support the passing of legislation which would mean "deal or no deal, the UK will exit the EU in March 2019".
Analysis: BBC Dublin correspondent Shane Harrison
Despite cordial exchanges between the two foreign ministers, one thing was clear: Ireland and the UK are still at odds about whether enough progress has been made in the EU-UK divorce talks to allow the two sides to move onto discussions about future relationships.
Despite British assertions that there will be no hard border on the island of Ireland, Dublin doesn't see how that position can be married with the UK leaving the customs union and the single market.
Nor does Dublin think a two-year transitional deal for business to adjust to Brexit is long enough.
With Taoiseach Leo Varadkar delivering the same message to Theresa May in Sweden, there is a sense that "make-your-mind-up time" for all sides is fast approaching.
During his talks in Dublin, Mr Johnson said it was necessary to move on to the second stage of negotiations, where issues raised by Mr Coveney would be thrashed out.
"Now is the time to make haste on that front," the UK foreign secretary said.
Mr Coveney said he understood the British "aspiration" to avoid a hard border, but more clarity was needed about the future.
"We are in the heat of the negotiations right now and, of course, we want to move on to the negotiations on trade, but there are issues that need more clarity," he said.
'Different rule book'
"This is a very fundamental change in the relationship between Ireland and Britain and Britain and the EU and it will require significant adjustment.
"The appropriate timetable is closer to four or five years than it is to two."
Contradictory messages from @simoncoveney & Boris Johnson over both the speed of any Brexit transition & whether negotiations between UK & EU should move on to phase 2 dealing with future trade relationships— Mark Devenport (@markdevenport) November 17, 2017
Mr Coveney added: "We simply don't see how we can avoid border infrastructure.
"Once standards change it creates differences between the two jurisdictions and a different rule book.
"When you have a different rule book you are starting to go down the route of having to have checks."
Asked whether the government was constrained by its confidence and supply arrangement with the Democratic Unionist Party, Mr Johnson said that was "not at all an issue".
The DUP agreed to support Theresa May's minority government after June's election in return for £1bn of extra funding for Northern Ireland.
European leaders say talks can only progress if enough progress has been made on the Irish border, citizens' rights and Britain's EU budget contributions.
Meanwhile, Ken Clarke has said the UK remaining in the single market and customs union is vital for peace and stability in Northern Ireland.
It is the obvious solution as no-one wants physical border controls, the former chancellor and now Conservative "rebel" told BBC NI's The View.
"The border problem in Northern Ireland, the supreme importance of keeping the settlement in place, retaining peace in Northern Ireland is probably the single biggest, most important reason why it would be preferable for the United Kingdom as a whole to stay in the single market and the customs union," he said.
"If the Brexiteers, these right-wing nationalists, won't allow us to do that then the best solution after that, I agree with the taoiseach actually, is to have a border down the Irish Sea."