Such words left a huge rift between the sides, just as Mr Johnson was preparing to visit German Chancellor Angela Merkel in Berlin on Wednesday and French President Emmanuel Macron in Paris on Thursday.
"The backstop is an insurance to avoid a hard border on the island of Ireland unless and until an alternative is found", Mr Tusk wrote.
Britain's Prime Minister Boris Johnson wrote that time is short and proposed that the backstop should be replaced with a commitment to put in place (alternative) arrangements as far as possible before the end of the transition period, as part of the future relationship.
Merkel, Europe's most powerful leader, said the European Union would consider "practical solutions" but that the Withdrawal Agreement, which contains the protocol on the Irish border "backstop", did not need to be changed.
Meanwhile Tony Lloyd, the party's shadow Northern Ireland secretary, has remarked that Johnson appears to have "forgotten that he voted for Theresa May's deal including the backstop." .
Under the current text of the Withdrawal Agreement, the backstop would be invoked at the end of the transition period in 2020, creating a single EU-UK customs territory, including "level playing field" rules ensuring fair competition in areas such as environment, state aid and labour standards.
But European Commission spokeswoman Natasha Bertaud said the letter "does not provide a legal, operational solution to prevent the return of a hard border on the island of Ireland". "I hope they will see fit to compromise".
These could include trusted-trader schemes and electronic pre-clearing to take checks away from the border, he said.
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He also suggested the United Kingdom was ready to make "commitments" to give confidence that there would be no hard border if the new system was not ready before the end of the two-year transition period that would follow the UK's formal exit from the EU.
Johnson has vowed to leave the European Union "come what may" on October 31, with or without a deal aimed at softening the transition.
"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".
To replace the backstop, Mr Johnson called for "flexible and creative solutions to the unique circumstances on the island of Ireland".
It would see the United Kingdom, as a whole, enter into a customs union with the EU for an indefinite period and also see the north of Ireland adhere to EU single market rules on goods.
It will be a once-in-a-generation chance for a real change of direction potentially on the scale of 1945.' And, calling on the government to immediately release its no-deal impact assessments, he added: 'The Operation Yellowhammer dossier makes the chaos and damage that will be caused by Boris Johnson's no-deal Brexit crystal clear'.
It comes a month after their first phone conversation on July 30, nearly a week after Mr Johnson became prime minister.