He was speaking in Brussels after the latest round of talks with his counterpart, Dominic Raab.
Barnier also insisted that the question of the Irish border must be “de-dramatised”, with the onus on both sides to make clear “which controls are needed where and how this should be done”.
Addressing the same briefing, Raab said the UK had a “moral obligation” to people and it was “inconceivable” they would be “turfed out”.
The EU, he said, must match the UK's “ambition and pragmatism” if the gaps between them were to be overcome.
With Brexit talks now set to intensify over the coming weeks in order to meet an autumn deadline set by both sides, Barnier said the pair had focused on what needs to be done in their “three work streams”: a backstop solution for avoiding a hard border on the island of Ireland; the other outstanding issues of the withdrawal agreement, for instance the protection of existing geographical indications, among others; and the political declaration on our future relationship.
Barnier said, “Our teams will sit together again on Thursday to try and make progress. Last week, our teams already had a discussion on Ireland and Northern Ireland.
“We need a legally operational backstop solution in the withdrawal agreement. We must find pragmatic solutions, in line with the commitments made by UK Prime Minister Theresa May in December and March.
“We must de-dramatise the issue, and spell out which controls are needed, where, and how they should be done. Next time we meet, Dominic and I will take stock of this work.”
Barnier went on, “The negotiations are now entering the final stage. We have agreed that the EU and the UK will negotiate continuously from now on. And Dominic and I will meet regularly to take stock and move the negotiations forward.”
Barnier told reporters, “The principles of the EU in these negotiations are well-known and have been consistent for the last two years.
“They have been defined by the EU leaders, with a great sense of responsibility for the European project and the integrity of the single market. Also, the EU respects the choices made by the UK government.”
He said, “We can find common ground based on the EU principles on the one hand and, on the other hand, the choices made by the UK. As I said in July, we are more, far more advanced in defining that common ground for foreign policy and security than for the economic relationship.
“Our challenge for the coming weeks is to try and define an ambitious partnership between the UK and the EU - a partnership that has no precedent. This partnership has to respect the single market and the foundations of the European project.
“If this is well understood, we can conclude the negotiations successfully.”