Berlin did not comment on their conversation, but a Number 10 source was quoted claiming that the Chancellor told the Prime Minister that “the UK cannot leave [the EU] without leaving Northern Ireland behind in a customs union and in full alignment forever”.
The comments provoked anger from opposition parties and in Brussels, where the EU Council President Donald Tusk responded by tweeting: “Boris Johnson, what’s at stake is not winning some stupid blame game”.
EU leaders have given the UK little hope that a new set of proposals for the Irish border that amount to creating two trade frontiers for Northern Ireland - a customs border with the Republic, and a regulatory border with the rest of the UK - will be accepted ahead of a last-chance summit in Brussels on 17 October.
The Irish government has said the plans are not the basis for a deal, and reports on Monday night suggested EU chief negotiator Michel Barnier had briefed representatives of the 27 member states on a series of problems with the UK offer.
Briefing journalists on the call, a Downing Street source was quoted as saying: “The call with Merkel showed the EU has adopted a new position. She made clear a deal is overwhelmingly unlikely and she thinks the EU has a veto on us leaving the customs union.”
They added: “Merkel said that the PM should tell Northern Ireland that it must stay in full alignment forever, but that even this would not eliminate customs issues.
“It was a very useful clarifying moment in all sorts of ways. If this represents a new established position, then it means a deal is essentially impossible not just now but ever.
“It also made clear that they are willing to torpedo the Good Friday Agreement.”
In Berlin, a German government spokesperson said: "I can confirm that Chancellor Merkel and British PM Johnson spoke on the phone this morning. As usual, we do not report such confidential conversations."
Ms Merkel and the Irish deputy Prime Minister Simon Coveney are both due to take questions from journalists at separate press conferences today.
Responding to Downing Street’s comments, First Minister Nicola Sturgeon tweeted: "The UK government's attempts to shift the blame for the Brexit fiasco to anyone but themselves - today it's Merkel - is pathetically transparent."
And Labour’s shadow Brexit secretary Keir Starmer tweeted: "This is yet another cynical attempt by Number 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.
"It is now more important than ever that Parliament unites to prevent this reckless Government crashing us out of the EU at the end of the month."
Mr Tusk posted on twitter: “Boris Johnson, what’s at stake is not winning some stupid blame game.
“At stake is the future of Europe and the UK as well as the security and interests of our people.”
Using the Latin phrase for ‘where are you going’, He added: “You don’t want a deal, you don’t want an extension, you don’t want to revoke, quo vadis?