British Prime Minister Boris Johnson and the European Union's chief executive gave themselves until Sunday for last-ditch negotiations on a post-Brexit trade deal after failing to narrow differences during a "frank discussion" over dinner in Brussels.

"Very large gaps remain between the two sides and it is still unclear whether these can be bridged," a senior source in the British prime minister's office said in a statement. He said Johnson did not want to leave "any route to a possible deal untested," and so he and European Commission President Ursula von der Leyen had agreed to further discussions over the next few days between their negotiating teams.

However, Von der Leyen warned Wednesday that Brussels and London remain "far apart" on the terms for a post-Brexit trade deal.

"We had a lively and interesting discussion on the state of play across the list of outstanding issues," she said, after a working dinner with Johnson. "We gained a clear understanding of each other's positions. They remain far apart," her statement said.

The two sides agreed that a decision on whether a deal is possible before Britain finally leaves the EU's orbit on January 1 would be taken by the end of the weekend.

Fears are running high of a chaotic no-deal finale to the five-year Brexit crisis.

The EU and Britain had cast Thursday's meeting as a chance to break an impasse in negotiations but both acknowledged there was a danger that a trade deal would elude them.

Earlier Johnson said Brussels wanted Britain to comply with new EU laws in the future or be automatically punished, and was insisting it gives up sovereign control over its fishing waters.

"I don't believe that those are terms that any prime minister of this country should accept," he told the British parliament, to cheers from lawmakers in his Conservative Party.

The United States on Wednesday said Britain's departure from the EU means it cannot impose tariffs on Washington in a dispute over aviation industry subsidies.

"The UK did not bring a case in its individual capacity" but was rather part of the EU when the dispute was brought before the World Trade Organization (WTO), the U.S. Trade Representative (USTR) said in a statement.

"Therefore, the UK has no authority from the WTO to participate in any such action after it no longer is part of the EU."

Britain formally left the bloc in January, but has since been in a transition period during which it remains in the EU single market and customs union, meaning that rules on trade, travel and business have stayed the same. That ends on December 31. If by then there is no agreement to protect around $1 trillion in annual trade from tariffs and quotas, businesses on both sides will suffer.

(With inputs from Reuters and AFP)