Boris Johnson has been accused of having “no negotiating strategy” after repeating his Brexit demand for the Irish backstop to be scrapped in his first letter to Donald Tusk.

Just hours after one EU leader said the withdrawal agreement “cannot be reopened”, the prime minister described the deal negotiated by Theresa May’s government as “unviable”.

Mr Johnson said the problems with the backstop – the bloc’s insurance policy to prevent a hard border in Northern Ireland – “run much deeper than the simple political reality that it has three times been rejected” by the Commons.

In his four-page letter to the European Council president, he outlined his Brexit red lines, and said the backstop “cannot form part of an agreed withdrawal agreement”.

“This is a fact we must both acknowledge,” he wrote. “I believe the task before us is to strive to find other solutions, and I believe an agreement is possible.”

Ahead of talks with Emmanuel Macron and Angela Merkel in Paris and Berlin later this week, he described the backstop as “anti-democratic” and “inconsistent” with the UK’s plans for a future relationship with the EU.

Boris Johnson's cabinet: Who's in and who's out Show all 40 1 /40 Boris Johnson's cabinet: Who's in and who's out Boris Johnson's cabinet: Who's in and who's out In: Jacob Rees-Mogg Jacob Rees Mogg appointed Leader of the Commons AFP/Getty Boris Johnson's cabinet: Who's in and who's out In: Esther McVey Esther McVey appointed housing secretary AFP/Getty Boris Johnson's cabinet: Who's in and who's out In: Jo Johnson Jo Johnson appointed new business and energy secretary EPA Boris Johnson's cabinet: Who's in and who's out In: Brandon Lewis Brandon Lewis appointed immigration secretary Getty Boris Johnson's cabinet: Who's in and who's out In: James Cleverly James Cleverly appointed Conservative Party chairman PA Boris Johnson's cabinet: Who's in and who's out In: Baroness Evans Baroness Evans remains Leader of Lords PA Boris Johnson's cabinet: Who's in and who's out In: Julian Smith Julian Smith appointed Northern Irish secretary Reuters Boris Johnson's cabinet: Who's in and who's out In: Alister Jack Alister jack appointed Scottish secretary PA Boris Johnson's cabinet: Who's in and who's out In: Alun Cairns Alun Cairns remains Welsh secretary AFP/Getty Boris Johnson's cabinet: Who's in and who's out In: Grant Shapps Grant Shapps appointed transport secretary Getty Boris Johnson's cabinet: Who's in and who's out In: Alok Sharma Alok Sharma appointed international development secretary AFP/Getty Boris Johnson's cabinet: Who's in and who's out In: Robert Buckland Robert Buckland appointed justice secretary Getty Boris Johnson's cabinet: Who's in and who's out In: Amber Rudd Amber Rudd remains work and pensions secretary Getty Boris Johnson's cabinet: Who's in and who's out In: Robert Jenrick Robert Jenrick appointed housing and communities secretary AFP/Getty Boris Johnson's cabinet: Who's in and who's out In: Andrea Leadsom Andrea Leadsom appointed business secretary Reuters Boris Johnson's cabinet: Who's in and who's out In: Nicky Morgan Nicky Morgan appointed culture secretary Getty Boris Johnson's cabinet: Who's in and who's out In: Gavin Williamson Gavin Williamson appointed education secretary AFP/Getty Boris Johnson's cabinet: Who's in and who's out In: Theresa Villiers Theresa Villiers appointed environment secretary AFP/Getty Boris Johnson's cabinet: Who's in and who's out In: Liz Truss Liz Truss is appointed international trade secretary Reuters Boris Johnson's cabinet: Who's in and who's out In: Ben Wallace Ben Wallace appointed defence secretary EPA Boris Johnson's cabinet: Who's in and who's out In: Stephen Barclay Stephen Barclay remains EU secretary AFP/Getty Boris Johnson's cabinet: Who's in and who's out In: Dominic Raab Dominic Raab appointed foreign secretary AFP/Getty Boris Johnson's cabinet: Who's in and who's out In: Priti Patel Priti Patel appointed home secretary AFP/Getty Boris Johnson's cabinet: Who's in and who's out In: Michael Gove Michael Gove given Chandellor of the Duchy of Lancaster AFP Boris Johnson's cabinet: Who's in and who's out In: Sajid Javid Sajid Javid is appointed Chancellor of the Exchequer AP Boris Johnson's cabinet: Who's in and who's out Out: Jeremy Hunt Jeremy Hunt sacked as foreign secretary Reuters Boris Johnson's cabinet: Who's in and who's out In: Matt Hancock Matt Hancock remains health secretary AFP/Getty Boris Johnson's cabinet: Who's in and who's out Out: Chris Grayling Chris Grayling resigned as transport secretary Getty Boris Johnson's cabinet: Who's in and who's out Out: Jeremy Wright Jeremy Wright sacked as culture secretary PA Boris Johnson's cabinet: Who's in and who's out Out: Karen Bradley Karen Bradley sacked as Northern Ireland secretary Getty Boris Johnson's cabinet: Who's in and who's out Out: James Brokenshire James Brokenshire sacked as housing and communities secretary Reuters Boris Johnson's cabinet: Who's in and who's out Out: Penny Mordaunt Penny Mourdaunt sacked as defence secretary Reuters Boris Johnson's cabinet: Who's in and who's out Out: Liam Fox Liam Fox sacked as international trade secretary Getty Boris Johnson's cabinet: Who's in and who's out Out: Greg Clarke Greg Clarke sacked as business secretary PA Boris Johnson's cabinet: Who's in and who's out Out: David Mundell David Mundell sacked as Scottish secretary Getty Boris Johnson's cabinet: Who's in and who's out Out: Damien Hinds Damien Hinds sacked as education secretary Getty Boris Johnson's cabinet: Who's in and who's out Out: David Gauke David Gauke resigned as justice secretary EPA Boris Johnson's cabinet: Who's in and who's out Out: Rory Stewart Rory Stewart resigned as international development secretary Getty Boris Johnson's cabinet: Who's in and who's out Out: David Lidlington David Lidlington resigned as deputy Prime Minister PA Boris Johnson's cabinet: Who's in and who's out Out: Philip Hammond Philip Hammond resigned as Chancellor of the Exchequer AFP/Getty

But Sir Keir Starmer, the shadow Brexit secretary, said: “The letter confirms that [Mr] Johnson has no negotiating strategy. He suggests (unspecified) alternatives to the backstop. And if they don’t work: further (unspecified) alternatives to the backstop. Why didn’t anyone think of that before.”

Mr Johnson wrote: ”The backstop locks the UK, potentially indefinitely, into an international treaty which will bind us into a customs union and which applies large areas of single market legislation in Northern Ireland.

“The treaty provides no sovereign means of exiting unilaterally and affords the people of Northern Ireland no influence over the legislation which applies to them.”

He concluded his correspondence, adding: “Time is very short. But the UK is ready to move quickly, and, given the degree of common ground already, I hope that the EU will be ready to do likewise.

“I am equally confident that our parliament would be able to act rapidly if we were able to reach a satisfactory agreement which did not contain the ‘backstop’: indeed it has already demonstrated that there is a majority for an agreement on these lines.”

It comes after Mr Johnson insisted he was “confident” of securing fresh concessions from the EU27, who he claimed were “showing a little bit of reluctance at the moment to change their position”.

He continued: “That’s fine – I’m confident that they will – but in the meantime we have to get ready for a no-deal outcome. I want a deal. We’re ready to work with our friends and partners to get a deal, but if you want a good deal for the UK, you must simultaneously get ready to come out without one.”

Before sending the letter, Mr Johnson also held almost an hour-long phone call with his Irish counterpart, Leo Varadkar, with the two leaders agreeing to meet in Dublin early in September.

According to No 10, the prime minister indicated the Brexit withdrawal agreement in its current form will not get through the Commons, and that the “backstop would need to be removed”.