Irish Prime Minister Leo Varadkar has ruled out formal three-way talks between the UK, Ireland and the EU to look at Theresa May's Brexit offer.
Updating MPs on her plans, Mrs May said the UK and Irish governments and the European Commission "will be working together" to avoid a hard border on the island of Ireland.
But Mr Varadkar said it was not in Ireland's interests to take part in formal three-way talks regarding the wider Brexit issues, and that what was needed was for Downing Street to produce more detailed proposals.
He said talks would be limited to issues unique to Ireland.
Mrs May set out her position in the Commons following last week's major speech on Brexit.
She told MPs: "We will not go back to a hard border between Northern Ireland and Ireland.
"Neither will we break up the UK's own common market with a border down the Irish Sea.
"As Prime Minister I am not going to let our departure from the EU do anything to set back the historic progress made in Northern Ireland, nor will I allow anything that would damage the integrity of our precious union.
"The UK and Irish governments and the European Commission will be working together to ensure that we fulfil these commitments."
But before Mrs May's statement, the Irish PM said: "There won't be tripartite or three-way talks.
"What will happen is that there will be talks between the EU 27 and the UK, and Ireland is part of the EU 27 and we're much stronger by the way as one of 27."
Mr Varadkar added consultations could take place between the two governments about issues that are unique to Ireland.
"We will of course have negotiations about what could be done to avoid a hard border, but what we won't be getting into is a negotiation with the UK, or a three-way negotiation," Mr Varadkar said.
"That's not in our interest and not the way that this can be concluded."
The Taoiseach told RTE's Morning Ireland programme that he gave Mrs May's Brexit speech on Friday a guarded welcome, but that detail was now needed from the UK Government.
"What we want is not so much principles and aspirations and red lines," Mr Varadkar said.
"What we want is detail, written down in black and white that can be codified into law and that is what is required."
Mrs May's speech earned her breathing space from warring Remain and Leave factions in the Conservative Party, but her plans for maintaining a soft Irish border while leaving the customs union were thrown into doubt when Irish Tanaiste and foreign minister Simon Coveney said the EU may not accept her proposals.
Amid the ongoing row over the border, Sinn Fein leaders Mary Lou McDonald and Michelle O'Neill travelled to Brussels on Monday to meet EU chief negotiator Michel Barnier.
After what she described as a "frank, productive and positive" meeting with Mr Barnier, Mrs McDonald voiced support for the Taoiseach's stance.
"The Taoiseach is absolutely correct to say that the substantive negotiation is between the British government on one hand and the EU member states collectively on the other and in our view it is important to maintain that dynamic," she said.
The Sinn Fein president added: "The ball is now in Mrs May's court, the ball is now in the court of the British, who say they don't like what they have seen, they don't like the solution advanced by Europe, if they don't like that we would like to know what is their solution."
Mrs McDonald said Mr Barnier understood the importance of resolving the border problem.
"I am happy to say we have a shared understanding that there cannot be a withdrawal agreement, much less an agreement on any future relationship between Britain and the European Union, in the absence of an answer to the Irish question," she said.
Mr Barnier, who is due to meet DUP leader Arlene Foster and deputy leader Nigel Dodds in Brussels on Tuesday, said his discussions with Sinn Fein had been positive.
He tweeted: "Essential to listen to all voices in Northern Ireland."
Mrs May has rejected Brussels proposals that would see Northern Ireland kept in an effective customs union with the EU as a fallback in case other solutions cannot be found.
She has proposed technological solutions and an exemption from new restrictions on the 80% of cross-frontier trade carried out by smaller businesses.
Mrs May told MPs: "We cannot escape the complexity of the task ahead.
"We must build a new and lasting relationship while preparing for every scenario.
"But with pragmatism, calm and patient discussion, I am confident we can set an example to the world."