The European Union's chief negotiator Michel Barnier warned on Tuesday that any long Brexit delay would pile on economic and political costs for the bloc.

Barnier asked if any potential postponement of the UK's departure date of March 29 would be useful. "We cannot prolong uncertainty without having a good reason for it," Barnier told reporters on Tuesday, 10 days before Brexit day as it stands in UK law.

"EU leaders will need a concrete plan from the UK in order to be able to make an informed decision," Barnier said.

A spokesman for UK Prime Minister Theresa May said the PM would write to European Council President Donald Tusk ahead of an EU leaders' summit on Thursday with a plan for delaying Brexit, but did not provide specifics.

EU diplomats have expressed concern that delaying without a plan could succeed only in "prolonging the agony" of the current deadlock in the UK Parliament.

"The clock is ticking and time is running out and we are really exhausted by these negotiations," German EU Affairs Minister Michael Roth told journalists. He said that, in Germany's view, the EU cannot grant an extension without "clear and precise proposals" from London.

"It's not just a game. It's an extremely serious situation," he added, saying that the mood among member states was "very bad."

"It will be for the Prime Minister and Her Majesty's Government to decide on the next steps and then to inform us accordingly and swiftly," spokesman Margaritis Schinas said.

French EU Affairs Minister Nathalie Loiseau echoed those comments, saying the time for a decision had come: "We are approaching this with goodwill. But we also have other issues to deal with and we have fellow citizens and businesses for whom the uncertainty is unbearable."

German Chancellor Angela Merkel said she was prepared to struggle until the last possible moment to secure an orderly exit for Britain, saying a no-deal divorce would be detrimental to all sides.

"I will fight to the last hour of the deadline on March 29 for an orderly exit [of Britain from the European Union]," she told a conference in Berlin. "We don't have a lot of time for it but still have a few days."

German Foreign Minister Heiko Maas stressed that he would rather give the UK more time to find a solution than end up with a no-deal scenario: "If more time is needed, it's always better to do another round than a no-deal Brexit," Maas told a news conference in Helsinki.