The stalemate will stoke fears swirling in London and Brussels of a breakdown in talks that could see Britain leaving the European Union in March 2019 without an agreement to soften the blow.
Wrapping up a fifth round of talks with Britain's David Davis, Barnier said he could not recommend to EU leaders at a summit next week that negotiations move on from divorce issues to talks on a post-Brexit trade deal.
"We are at a deadlock on this question which is extremely disturbing," Barnier said at a press conference with Davis at the European Commission headquarters in Brussels.
Speaking a mix of French and English, Barnier said the "constructive" talks had clarified some points but there had not been any "great steps forward" on central issues.
The leaders of the 27 other EU countries have demanded there be "sufficient progress" on the Brexit bill, the rights of EU citizens living in Britain, and on Northern Ireland before moving on to discuss a post-Brexit trade deal.
"I am not currently able to recommend to next week's European Council to open discussions on the future relationship," Barnier said.
But he added: "I remain convinced that with political will, decisive breakthroughs are within reach in the coming two months."
He also warned against the possibility of a so-called "hard Brexit" after May admitted this week that her government was setting aside money for a "no-deal scenario".
"A no deal will be a very bad deal," Barnier said.
May later said the two sides were "very close to agreement" on a number of issues including citizens' rights and welcomed Barnier's recognition that progress could be made in the coming weeks.
"I hope the member states will recognise the progress we've made and take a step forward in the spirit of the prime minister's Florence speech," Davis said, adding that it was "in the interests of Europe and the UK."
He called on EU leaders to give Barnier a mandate next week to "explore ways forward" on May's proposal for a two- year transition period after Brexit, even if trade talks are not opened.
EU President Donald Tusk warned Tuesday that the bloc might rethink whether a Brexit deal is possible if there is no progress by the end of the year.
Tusk also ruled out the possibility of moving onto the trade talks phase at the October 19 summit, though he said he hoped to be able to by the next summit in December.
"If it turns out that the talks continue at a slow pace, and that 'sufficient progress' hasn't been reached, then -- together with our UK friends -- we will have to think about where we are heading," he said.
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