Speaking after Mr Barnier's address to the General Affairs Council, Bulgarian deputy prime minister Ekaterina Zaharieva said: "What the United Kingdom proposed doesn't mean there is no hard border".
As reported by the Independent, the renewed deadlock in Brussels comes as Theresa May's cabinet repeatedly fails to agree with itself on what customs arrangement it wants with the European Union after Brexit, despite publishing two options in August of past year.
According to Zakharieva, "substantive progress" needs to be achieved on Ireland, governance, and all remaining separation issues by next month.
About it reports Reuters with a reference to the statement by the German Minister for European Affairs Michael Roth announced in Brussels on Monday, may 14.
"Time is passing. We must now make substantial progress".
"We are concerned that there is no clear stance, no clear position from the British".
The shadow Foreign Secretary said: "Can I begin by thanking the Foreign Secretary for leading our cross-party efforts over the last two weeks to destroy the Prime Minister's customs partnership proposal?" Foreign Secretary Boris Johnson has branded the Prime Minister's idea "crazy" and he and other detractors of the partnership concept instead contend that new technology and trusted trader schemes can provide for smooth cross-border trading.
Asked about the issue on Monday, a French presidential adviser said there was no decision from the European Union to exclude Britain from Galileo, and that the current "uncertainty" was simply the direct result of Britain's decision to leave.
While both sides want to continue close cooperation on internal security and foreign policy after Brexit, even this area, previously seen as an easy part of the unprecedented divorce negotiations, has seen a series of recent hiccups.
But the European Union has said London must come up with a solution for the Irish border conundrum and highlights that has not happened.
Mr Johnson said Ms Thornberry had failed to be clear over Labour's policy, claiming the government had been "absolutely clear" and said prime minister Theresa May has said "time and time again" that the United Kingdom was leaving the single market and customs union while "taking back control" of borders, laws and money.
Other outstanding issues include guarantees for expatriate rights, agreeing on security cooperation and trade rules after Brexit, to ensure a deal is in place when Britain leaves in March 2019, and an adaptation period ends at the end of 2020.