Brexit negotiations "have been difficult" and "no solution has been identified" to the Irish backstop, the European Commission has said.
Commission spokesman Margaritis Schinas said the talks had taken place in a "constructive atmosphere" but there had been no breakthrough.
The UK is pushing for legally-binding changes to the EU deal.
Mr Schinas was speaking after Mr Barnier briefed the European Commission's weekly meeting on the state of Brexit talks.
Speaking after talks with Mr Barnier, the UK's Attorney General Geoffrey Cox said: "Both sides have exchanged robust, strong views. We're now facing the real discussions. Talks will be resuming soon."
He added: "We're into the meat of the matter, we've put forward very reasonable proposals."
Downing Street echoed Mr Barnier's characterisation of the talks as "difficult", but said the negotiations were "ongoing".
"The EU continues to say that it wants this to be resolved and that it wants the UK to leave with a deal. Parliament has been clear that for this to happen, we require legally-binding changes which mean that the UK can't be trapped in the backstop indefinitely," said the PM's official spokesman.
"That is what we will continue to pursue."
The backstop is an insurance policy - designed to avoid a hard border "under all circumstances" - between Northern Ireland and the Irish Republic.
Prime Minister Theresa May is pinning her hopes on getting changes to it that will prevent the UK from being tied to EU customs rules if no permanent trade deal is agreed after Brexit.
She believes this would be enough to get MPs - who last month rejected her deal by an historic margin - to back her deal in a vote she has promised on or before 12 March.
Source: BBC News.