Gerry Adams has said Ireland should prevent Brexit talks on links between Britain and the EU.
he Sinn Fein leader claimed Britain's plans so far were unworkable and unrealistic.
The EU has decided that discussions on its future relationship with Britain, including trade, can only start once sufficient agreement is reached on issues like the Irish border.
In the latest round of negotiations genuine progress was made on issues like maintaining freedom of movement for citizens of the two countries between the UK and Ireland, Europe's chief Brexit negotiator Michel Barnier said - but he added no decisive breakthrough had been made.
Mr Adams said: "The fact that no definitive progress has been made in these talks is evidence that the British Brexit plans are unworkable and unrealistic.
"The Irish government should insist that the negotiations are not ready to move to the next stage."
The UK's only land frontier with an EU state post-Brexit will run between Northern Ireland and the Republic and citizens of both countries fear they could be particularly disadvantaged. Irish citizens living in Great Britain have also raised concerns.
A good discussion was held on retaining the open border between the Republic and Northern Ireland, British Brexit Secretary David Davis said.
Mr Barnier said: "We have made genuine progress on the question of the Common Travel Area (CTA), on the basis of guarantees from the United Kingdom."
The CTA is a decades-old deal between Britain and Ireland ensuring freedom of movement of people from both countries.
In Brussels, Mr Davis said they had a good discussion on maintaining it and on safeguarding the 1998 Good Friday Agreement which largely ended violence in Northern Ireland, on the basis of a UK paper.
"We think there is a high degree of convergence on these key issues, and we agreed to work up shared principles on the Common Travel Area."
Chancellor Philip Hammond was in Ireland on Thursday to meet the Irish Foreign Affairs and Trade Minister Simon Coveney.
Mr Coveney said he had "urged" the Chancellor to "listen to those who stand to be most negatively impacted by Brexit across these islands".
"The Government is determined to avoid a hard border on the island of Ireland and to maintain to the greatest extent possible the status quo.
"I have reminded the Chancellor of the Irish Government's conviction that the UK remaining in the Customs Union and the Single Market is the best way in which this can be achieved."
He reiterated the Government's objective that there should be no new impediments to the all-island economy which has been able to develop over the last two decades as part of the peace process.
In an article for The Irish Times, published on Thursday, Mr Hammond said the British and Irish economies were "already closely entwined" and that the Government is "clear in our determination to avoid any physical border infrastructure on either side of the Border between Ireland and Northern Ireland".
He added: "After Brexit, goods must be able to move smoothly across the Border between the UK and Ireland, but so too must people."