In its position paper, published on Thursday, the European Union said "it's the responsibility of the United Kingdom" to ensure that Brexit protects the special "political, economic, security, societal and agricultural context and frameworks on the island of Ireland".
The UK has argued that especially the Ireland question can not be disentangled from other issues, such as customs and future trade deals, and therefore these negotiations should run in parallel.
"It is Britain taking a decision to stay in a customs partnership or stay in something similar, or not very different from the single European market, for a transitional period, and that is something I have said consistently and that is still my view".
Barnier's remarks came in a week after the third round of Brexit talks concluded last Thursday without no decisive progress, except some technical agreements on such issues as the future Irish border.
Ireland dismissed British proposals for the Irish border after Brexit as unconvincing on Friday as concerns continue grow over the re-establishment of a physical border between the Irish Republic and the British province of Northern Ireland possibly reviving old tensions.
The problem is that the United Kingdom has stated it wants to leave both the internal market and the customs union, while keeping trade for small companies unchecked and free movement between Northern Ireland and the republic.
Speaking in Brussels after a week of leaks in the British newspapers, and two days after Britain's Brexit negotiator debriefed parliament, Barnier warned that the bloc would not allow Britain to use Ireland as "a kind of test case" for future customs arrangements.
The Labour MSP added: " The talks do not appear to be making as much progress as had been expected by this point of time.
Brexit Secretary Mr Davis has insisted discussions with Brussels on border plans have been "good" but the EU's chief negotiator Mr Barnier, said "a lot more substantial work" needs to be done.
However, Mr Johnson told reporters that a solution to the problem of the Irish border would be found between the negotiating parties and made light of the EU's fears.
Guy Lougher of Pinsent Masons, the law firm behind Out-Law.com said: "The Commission's paper doesn't materially progress things".
It intends to explore with the European Union the option of a cross-border trade exemption and the streamlining of administrative processes for businesses not eligible for any such exemption.
Michel Barnier has said the United Kingdom appears to be "backtracking" on its financial obligations, saying he is "very disappointed" by comments made recently.
Q. So we're not any further forward on the border issue?