EU Brexit negotiator Michel Barnier says "no decisive progress" has been made on key issues, in the latest round of talks with the UK.
He said the two sides were "quite far" away from being in a position to begin talks on future trade arrangements.
But UK Brexit Secretary David Davis urged the EU to be "more imaginative and flexible" in its approach.
He said in his opinion there had been "some concrete progress" during the third round of talks in Brussels.
During a joint press conference, Mr Barnier acknowledged there had been some "fruitful" discussions on the issues surrounding the relationship between the Republic of Ireland and Northern Ireland, but he struck a pessimistic tone overall.
He claimed the UK did not feel "legally obliged" to honour its "obligations" after leaving the bloc in March 2019.
He also stressed that he was "impatient… I am not angry… I am impatient and determined" about the progress of negotiations.
But Mr Davis said more flexibility was needed to get a good deal for both sides.
"Beyond the debates about process and technicalities, at the heart of this process, must be a desire to deliver the best outcome for the people and the businesses of the European Union and the United Kingdom," he added - particularly on citizens' rights.
The UK wants to begin trade talks as soon as possible, but Brussels insists that discussions about the future relationship after Brexit can only begin once "sufficient progress" has been made on the arrangements for withdrawal - including on the so-called "divorce fee".
Mr Barnier said that at the current rate of progress, he was quite far from being able to recommend opening parallel talks on a future trade relationship with the UK.
He cited two areas where "trust" needed to be built between the two sides - on citizens' rights and the financial settlement, stressing that 27 members of the bloc should not have to pay for obligations taken by 28.
Claiming there had been a shift in the UK government's approach, he said: "In July the UK recognised that it has obligations beyond the Brexit date but this week the UK explained that these obligations will be limited to the last payment to the EU project before departure."
No figure has yet been put on the payment, but European Commission president Jean-Claude Juncker has suggested it could come in at around 60 billion euro (£55bn), while unconfirmed reports have put it as high as 100 billion euro (£92bn).
Mr Davis defended the "rigorous" line-by-line examination of the EU's demands carried out by British officials in response to the "unspecified but undoubtedly large" sum demanded by Brussels.
He added: "It will, of course, lead to difficult exchanges - nobody will pretend it was anything but a tough exchange this week - but I think the British taxpayer would expect nothing less."
Mr Davis also told reporters the talks had exposed how the UK approach was "substantially more flexible and pragmatic than that of the EU".
"This week we have had long and detailed discussions across multiple areas and I think it's fair to say we have seen some concrete progress, and Michel referred to one but there's more than that," he said.
"However, as I said at the start of the week, it's only through flexibility and imagination that we will achieve a deal that works truly for both sides.
"In some areas we have found this from the [European] Commission's side, which I welcome, but there remains some way to go."