European Council president has rebuffed 's request to remove the Northern Ireland backstop from the Brexit deal, instead suggesting the prime minister is actually supporting the return of a hard border by not proposing a realistic alternative.
It comes after the PM wrote to Mr Tusk on Monday evening outlining his opposition to what he called the “anti-democratic” Northern Ireland backstop.
Mr Tusk responded on Twitter, writing: "The backstop is an insurance to avoid a hard border on the island of Ireland unless and until an alternative is found.
"Those against the backstop and not proposing realistic alternatives in fact support reestablishing a border. Even if they do not admit it."
As ITV News Political Correspondent Paul Brand says, Mr Tusk's response seems to be "accusing the PM of being disingenuous about his aims".
In Mr Johnson's letter, he said while he wants the UK to leave the EU with a deal, he could not support any withdrawal agreement that "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".
German Chancellor Angela Merkel appeared to welcome Mr Johnson's eagerness to resolve the backstop by saying "when one has the will to find these solutions, one can do so in a short period of time."
But she said solving the backstop issue would not require the Withdrawal Agreement to be reopened and it would instead need resolving in the political declaration on future ties.
Labour leader Jeremy Corbyn said Mr Johnson needed to "wise up and stop the nonsense with October 31".
He said: "It's very unclear what the prime minister thinks he's negotiating.
"He needs to recognise that by just holding the threat of a no-deal Brexit by October 31 towards the European Union, isn't going to bring about a change, it's going to make things much worse."
He added however that he hopes Parliament will be able to stop no deal by supporting a motion of no confidence.
European Commission spokeswoman Natasha Bertaud said: "We welcome the UK Government's engagement and continued commitment to an orderly withdrawal. We firmly believe this is in the best interests of both the EU and the UK.
"However, we also note that the letter does not provide a legal operational solution to prevent the return of a hard border on the island of Ireland.
"It does not set out what any alternative arrangements could be and in fact it recognises that there is no guarantee that such arrangements will be in place by the end of the transitional period."
The European Parliament's Brexit co-ordinator Guy Verhofstadt tweeted: "I don't see any majority in the @Europarl--EN to remove the backstop from the Withdrawal Agreement.
"It is a vital insurance policy, negotiated in good faith & supported by the people of the Island of Ireland. The time for bluster & political blame games is fast running out."
Following a meeting of Mr Johnson's Exit Strategy committee, Transport Secretary Grant Shapps said the government wants a deal with the EU but "can't say whether we'll get one or not".
It comes after Irish premier Leo Varadkar also rejected Mr Johnson's call to reopen the Withdrawal Agreement during a telephone conversation with the Prime Minister on Monday.
During the call the pair "shared perspectives on the Withdrawal Agreement" and Mr Johnson said free movement between the UK and Ireland will not end in the event of a no-deal Brexit.
On the phone call a Downing Street spokesperson said: "The Taoiseach reiterated the EU27 position that the Withdrawal Agreement cannot be reopened, and emphasised the importance of the legally operable guarantee to ensure no hard border and continued free trade on the island of Ireland."
Mr Johnson will meet German Chancellor Angela Merkel on Wednesday and France's Emmanuel Macron on Thursday for his first face-to-face talks with Europe's key powerbrokers.
Writing to Mr Tusk, the PM confirmed he is committed to ensuring there is no return to a hard border on the island of Ireland.
He proposed “flexible and creative solutions to the unique circumstances on the island of Ireland”.
He added: “I propose that the backstop should be replaced with a commitment to put in place such arrangements as far as possible before the end of the transition period, as part of the future relationship.
“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.
“We are ready to look constructively and flexibly at what commitments might help, consistent of course with the principles set out in this letter.”
Mr Johnson acknowledged that “time is very short” but said: “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.”