Britain and Brussels appeared far apart on agreeing a future trade arrangement after the UK's chief negotiator said "very little" progress had been made in the latest round of talks.
David Frost insisted the major obstacle to agreement was the EU's insistence on including a set of "novel and unbalanced proposals" regarding a level playing field on standards.
Mr Frost also said it is "hard to understand why the EU insists on an ideological approach" to negotiations on fishing rights.
The EU's chief negotiator Michel Barnier insisted that the UK could "not have the best of both worlds" in a deal as he said the talks failed to produce any progress on the more difficult subjects.
Following the conclusion of the third negotiating round, Mr Frost said: "I regret, however, that we made very little progress towards agreement on the most significant outstanding issues between us.
"It is very clear that a standard comprehensive free trade agreement, with other key agreements on issues like law enforcement, civil nuclear, and aviation alongside, all in line with the Political Declaration, could be agreed without major difficulties in the time available.
"The major obstacle to this is the EU's insistence on including a set of novel and unbalanced proposals on the so-called 'level playing field' which would bind this country to EU law or standards, or determine our domestic legal regimes, in a way that is unprecedented in free trade agreements and not envisaged in the Political Declaration.
"As soon as the EU recognises that we will not conclude an agreement on that basis, we will be able to make progress."
Chief UK negotiator Mr Frost said fishing arrangements are another sticking point.
He said: "Although we have had useful discussions on fisheries on the basis of our draft legal text, the EU continues to insist on fisheries arrangements and access to UK fishing waters in a way that is incompatible with our future status as an independent coastal state.
"We are fully committed to agreeing fishing provisions in line with the Political Declaration, but we cannot agree arrangements that are manifestly unbalanced and against the interests of the UK fishing industry. It is hard to understand why the EU insists on an ideological approach which makes it more difficult to reach a mutually beneficial agreement."
Prime Minister Boris Johnson has repeatedly said he will not extend the post-Brexit transition period beyond its scheduled conclusion at the end of the year. Any such extension would need to be agreed by July 1.
Speaking at a press conference in Brussels, Mr Barnier said: "You cannot have the best of both worlds."
Mr Barnier continued: "With the exception of some modest overtures, we failed to make any progress on any of the other more difficult topics.
"Despite its claims, the United Kingdom did not engage in a real discussion on the question of the level playing field - those economic and commercial 'fair play' rules that we agreed to, with Boris Johnson, in the Political Declaration.
"On this topic, this was a round of divergence, with no progress.
"With regard to the governance of our future relationship, the few useful discussions we had were limited to sectorial questions."
Mr Barnier added: "The next round must bring new dynamism in order to avoid a stalemate between us.
"Let us make a success of round four in the first week of June by making the tangible progress we need."