"Very little progress" has been made in the latest round of UK-EU trade talks, the UK government has said.
The UK's negotiator David Frost said a far-reaching free trade agreement could be agreed before the end of the year "without major difficulties".
But it was being held up by the EU's desire to "bind" the UK to its laws and seek unfair access to fishing waters.
The EU's Michel Barnier suggested the UK's own demands were "not realistic" and warned of a looming stalemate.
Speaking in Brussels, the bloc's chief negotiator said "no progress had been made on the most difficult issues".
Asked by the BBC's Europe editor Katya Adler what the chances were of an agreement. Mr Barnier said he was "still determined but not optimistic".
The EU, he added, would not accept a deal "at any price" and it was stepping up preparations for a no-deal outcome, in which the two sides would trade with each other under World Trade Organisation rules.
Insisting the EU would not negotiate "in haste", he said the UK must consider whether it was feasible to strike a deal before the end of 2020, when the current 11-month transition period is due to end.
The UK has said it will not extend the process beyond 31 December, despite coming under growing pressure at home to allow more time for a deal due to the coronavirus pandemic.
The two sides have been discussing their future economic and security partnership following the UK's withdrawal from the 27-member bloc on 31 January.
In a statement, Mr Frost said there was a "good understanding" between the negotiators but that little or no progress had been on the most "significant outstanding issues".
The dancing's over
Analysis by Gavin Lee, Brussels reporter
Former EU Commission President Jean-Claude Juncker used to describe Brexit talks as being like a "dance" and regularly rolled out the stock phrase that "it takes two to tango".
There's no dancing anymore. Today Michel Barnier made clear he'd rejected any such romantic terms for these trade negotiations, telling reporters it was neither "a dance nor a tango or any other kind of dance".
He said the teams weren't "even in the same room" and this wasn't nearly as effective as getting together around a table.
The hours of screen time have led to an impasse, with both sides now urging the other to change strategy, and to understand the other's position more clearly.
I spoke to Spanish and French diplomats in Brussels. "Quelle surprise" was the view. They believe both sides will "continue to play tough and offer little ground" and that genuine compromise may come in a month, for the fourth and final scheduled round before the summer.
But few officials here are following the twists and turns with the dedication of the past. The urgency of dealing with the pandemic has reduced the attention to Brexit.
He said the EU was insisting upon a "set of novel and unbalanced proposals" in relation to competition issues that went well beyond other comparable trade agreements struck with other major economies.
The UK, he said, would not agree to "a so-called level playing field which would bind this country to EU law or standards, or determine our domestic legal regimes".
A level-playing field is a term for a set of common rules and standards that prevent businesses in one country undercutting their rivals and gaining a competitive advantage over those operating in other countries.
The EU, Mr Frost added, was seeking continued access to UK fishing waters after the transition period "in a way that is incompatible with our future status as an independent coastal state".
"It is hard to understand why the EU insists on an ideological approach which makes it more difficult to reach a mutually beneficial agreement," he said.
"We very much need a change in EU approach for the next round beginning on 1 June.
"The UK will continue to work hard to find an agreement, for as long as there is a constructive process in being, and continues to believe that this is possible."
Open and fair'
Mr Frost said the UK would make public all its draft legal texts next week so EU member states and interested observers "can see our approach in detail".
In his update, Mr Barnier said the EU's aim was a "modern, forward-looking" agreement which would avoid any tariffs or quotas on trade.
But he said it was not prepared to "copy and paste" aspects of existing agreements with Canada, Japan and South Korea or do sector-by-sector deals "rooted in past precedents".
Tariff-free access to the EU's single market had to be accompanied by obligations, he added, and the UK could not "pick and choose" which of these it adhered to.
"You cannot have the best of both worlds," he said. "Open and fair competition is not a nice to have. It is a must-have."
A "new dynamism" would be needed in the next round of talks to deliver "tangible progress", he added.
Mr Barnier said he would listen to concerns the UK had about the treatment of British expats on the continent as part of the implementation of the Withdrawal Agreement governing the terms of the UK's exit.