"In his letter, Johnson described the backstop as "inconsistent with the sovereignty of the UK", adding that the arrangement would be "anti-democratic" because it offered no means for the United Kingdom to unilaterally exit and no say for the people of Northern Ireland over the rules that would apply there".
In a phone conversation with Johnson on Monday evening, Irish Taoiseach (Prime Minister) Leo Varadkar reiterated that the agreement could not be reopened and the backstop could not change, the BBC reported.
A diplomat from one European Union country told Reuters that Johnson's letter was "pure PR" and not meant to spur constructive talks but rather set the stage for a "blame game" with the EU.
In the diplomatic note obtained by The Associated Press, the EU's remaining 27 nations were strongly urged not to give in to Mr Johnson's demand that the legal withdrawal agreement the European Union negotiated with his predecessor, Theresa May, be changed at this late stage.
The riddle of what to do about Ireland's 500-km (300-mile) land border with the British province of Northern Ireland remains has repeatedly imperilled Brexit talks.
But, in a tweet on Tuesday, Donald Tusk replied, saying, "The backstop is an insurance to avoid a hard border on the island of Ireland unless and until an alternative is found". The letter penned by the UK PM was underpinned by the overarching demand that the contentious Irish backstop be ripped up and replaced with something else. "Those who are against it and do not propose realistic alternatives actually support the reintroduction of a border".
In the letter, Mr Johnson said while he wants the United Kingdom to leave the EU with a deal, he could not support any withdrawal agreement that "locks the United Kingdom, potentially indefinitely, into an worldwide treaty which will bind us into a customs union and which applies large areas of single market legislation in Northern Ireland". "Even if they do not admit it", Tusk wrote on Twitter.
The EU's diplomatic note said it needed to counter Mr Johnson's assertions, insisting "it is incorrect to state that the people of Northern Ireland have no influence over the legislation that would apply to them".
With British politics in such turmoil, it is still unclear how, when or indeed if the United Kingdom will leave the EU.
Mr Johnson will meet German Chancellor Angela Merkel on Wednesday and France'sEmmanuel Macron on Thursday for his first face-to-face talks with Europe's key powerbrokers.
"At the moment it is absolutely true that our friends and partners are a bit negative ... but I think we'll get there", he said.
"I also recognise that there will need to be a degree of confidence about what would happen if these arrangements were not all fully in place at the end of that period".
But he is facing rising criticism of his Brexit strategy at home. Johnson's government is propped up by Northern Irish unionists.
After a 2016 referendum in which the public voted to leave the EU, Mrs May spent more than two years negotiating a Brexit divorce agreement with the bloc.