Tánaiste has said the British Government's position on Brexit has become much more credible following the publication of its White Paper today.
However Simon Coveney warned that while it is important to recognise progress, the negotiations ahead would be difficult.
He added that there are some contradictions and proposals in the White Paper that would concern other EU countries.
"I don't believe that Michel Barnier [EU’s chief negotiator] will, or will be allowed, to compromise the functioning of the single market or to compromise the functioning of a common customs union.
"So that I think will be the real challenge for the negotiating teams over the summer. But nobody said this was going to be easy," he said.
Mr Coveney said too that today's publication is a step towards a much softer Brexit than many in the UK had been advocating for.
"I think we should hopefully see the Brexit process move from the politics of parliaments to the negotiating rooms in Brussels... which is hopefully where we will get to from Monday on," he said.
Meanwhile Sinn Féin Leader Mary Lou McDonald said that the UK government's White Paper does not give the certainty that Ireland needs.
However, she said it does signal the opportunity for a very serious negotiation.
These talks must provide the legal clarity to protect Ireland and this must happen before the October European Council summit, Ms McDonald said.
This evening, the EU's chief negotiator, Michel Barnier said his team would now analyse the UK's White Paper and he said he looked forward to next week's talks with his British counterparts.
Speaking in the United States, Mr Barnier said: "We are going to assess this white paper in line with the guidelines of the 27 leaders of the EU and also to check the workability of this proposal."
We will now analyse the #Brexit White Paper w/ Member States & EP, in light of #EUCO guidelines. EU offer = ambitious FTA + effective cooperation on wide range of issues, including a strong security partnership. Looking forward to negotiations with the #UK next week.— Michel Barnier (@MichelBarnier) July 12, 2018
Mr Barnier is meeting with members of the US Congress in Washington this evening.
He is on Capitol Hill to brief members of the 'Friends of Ireland' group of representatives.
The Frenchman is due to give delegates an update on Brexit negotiations and also discuss implications for the Good Friday Agreement and the border on the island of Ireland.
Earlier, the UK's government blueprint for future ties with the EU was described as a bad deal for Britain and "the greatest vassalage since King John paid homage to Phillip II at Le Goulet in 1200".
Britain's new Brexit minister told the House of Commons that it is now up to the European Union to respond to the document.
"Now, it is time for the EU to respond in kind, we approach these negotiations with a spirit of pragmatism, compromise and, indeed, friendship, I hope, I trust that the EU will engage with our proposals in the same spirit," he told the House of Commons
However, Conservative MP Jacob Rees-Mogg, the chair of the European Research Group of Tory eurosceptics, described the White Paper as "the greatest vassalage since King John paid homage to Phillip II at Le Goulet in 1200".
Mr Rees-Mogg said: "This White paper has not needed age to turn yellow. There are very few signs of the Prime Minister's famous red lines. It is a pale imitation of the paper prepared by David Davis, a bad deal for Britain. It is not be something I would vote for nor is it what the British people voted for."
Commons Speaker John Bercow said it was a "source of considerable unhappiness on both sides of the House" that the White Paper had not been made available earlier.
He said: "Members of Parliament should have a copy of the White Paper about which they are to question him."
Mr Bercow, suspending the House to allow MPs to collect the document, said: "I say to the Secretary of State that it would be very unseemly, discourteous to him and to the members of the House for his statement to be delivered while copies are being distributed, I therefore suspend the sitting of the House for five minutes.
"It is most regrettable that this situation has arisen, but I'm dealing in a way that I think is constructive with what has arisen."
Labour Party spokeperson on Brexit Keir Starmer said Mr Raab had "not got off to a very good start".
He said: "The utter shambles of the last 20 minutes that led to the suspension of the House during a statement is clear evidence of why the government is in such a mess."
He asked why the government thought it appropriate to share the White Paper with journalists at 9am this morning, "only to provide the opposition with a copy three hours later".
The new blueprint for Brexit is a "real blow" to London's all-important finance sector as it will damage jobs, tax revenues and growth, a City official said.
"Today's Brexit white paper is a real blow for the UK's financial and related professional services sector," Catherine McGuinness, policy chairman of the City of London Corporation, said in a statement.