The British government warned Tuesday that it will be “essentially impossible” to strike a Brexit deal with the European Union if the bloc continues to stand by a key trade demand involving Northern Ireland.

The grim assessment from Prime Minister Boris Johnson's office following a phone call between the British leader and German Chancellor Angela Merkel comes just weeks before an Oct. 31 deadline to leave the EU. The EU has been responding coolly to the U.K.'s plan for maintaining an open Irish border after Brexit, which has been the main stumbling block to a deal.

Downing St. said Merkel told the prime minister Tuesday morning that "a deal is overwhelmingly unlikely" unless Northern Ireland remains in a customs union with the EU — something the U.K. says it can't allow.

It added that "if this represents a new established position, then it means a deal is essentially impossible not just now but ever."

A European Union flag flies near Parliament in London on Tuesday. (AP)

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Currently, goods and people flow freely between EU member Ireland and the U.K.'s Northern Ireland. The EU and the U.K. have agreed there must be no checks or infrastructure along that border, yet Britain wants to leave the EU's customs union so it can strike new trade deals around the world, making some sort of checks on goods crossing that border all but inevitable.

Under a proposed U.K. Brexit plan there would be customs checks, but Britain says they could be conducted away from Northern Ireland’s border.

However, EU officials oppose any customs checks and are skeptical of U.K. claims they could be achieved through largely untested technology. EU leaders also have been sharply critical of a proposal that would give Northern Ireland's legislature an effective veto on key elements of the Irish border arrangements in the future.

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Johnson has urged European leaders to compromise and sit down for face-to-face talks. So far, the EU is resisting, saying the U.K. must show more "realism" in its proposals.

“At stake is the future of Europe and the UK, as well as the security and interests of our people,” European Council President Donald Tusk tweeted at Johnson on Tuesday, adding that “what’s at stake is not winning some stupid blame game.”

Britain's Prime Minister Boris Johnson speaks to mental health professionals during his visit to Watford General Hospital, in Watford, on Monday. (AP)

The last scheduled opportunity to reach a deal is Oct. 17-18, when all 28 EU leaders, including Johnson, are due to meet in Brussels. French President Emmanuel Macron has said the EU will decide by the end of this week whether a deal is possible, or whether the two sides should buckle up for a rocky no-deal departure.

Johnson insists the U.K. will leave the EU on Oct. 31 even without a deal. But many in the EU — and in Britain — are skeptical that Britain will leave the bloc that day, because the U.K. Parliament has passed a law compelling the government to ask the EU for a delay to Brexit if no deal is agreed upon by Oct. 19.

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Keir Starmer, the Brexit spokesman for the main opposition Labour Party, said Downing St.’s statement Tuesday was "yet another cynical attempt by No. 10 to sabotage the negotiations."

"Boris Johnson will never take responsibility for his own failure to put forward a credible deal. His strategy from Day One has been for a no-deal Brexit," he said.

The Associated Press contributed to this report.