"Obviously, we need further clarity if we can reach a sense of future relations", said Jean-Claude Juncker during a debate in the European Parliament in Strasbourg on the stalemate in talks with London.
The Federation of German Industry (BDI) urged British Prime Minister Theresa May and the remaining 27 European Union leaders to agree a "status quo" transition period preserving present trade arrangements beyond Britain's departure date of March 29, 2019.
As negotiators rush to strike an agreement on a post-Brexit transition period that the United Kingdom insists it needs this month, Barnier poured cold water on May's request to stick with some elements of EU membership while leaving its customs union and single market once the transition ends in 2021.
This will be the first one after the United Kingdom withdrawing from the EU.
Mr Juncker told MEPs: 'I would rather have preferred Britain not to have chose to leave the European Union, but anyone who leaves has to know, frankly, what this means'.
Juncker said the controversial "backstop" proposal for dealing with the border between Northern Ireland and the Republic "translates faithfully" the agreement reached between Mrs May and the European Union in December.
The suggestion that the Irish border is a European issue was heckled by one MEP, who shouted: "It is a British issue".
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Other sticking points will be avoiding a hard border in Ireland, as well as securing citizens' rights.
Mr Barnier added that it was a "rather surprising idea" to think the European Union could accept convergence in some areas "and at the same time open up the possibility for divergence when there is a comparative advantage to be had" for the UK.
"It sounds to me like they believe it was Russian Federation, and I would certainly take that finding as fact", he added.
"We're stuck inside a Customs Union".
"Do they also want to distance themselves from our regulatory model, the one that we have constructed together with you - and you with us - for 44 years?" "It's now time to translate speeches into treaties, turn commitments into agreements, and to move from the soundbite, broad suggestions and wishes on the future relationship to specific, workable solutions".
Another German industry group, the VDMA engineering association, also called on Tuesday for an EU-UK customs deal.