In a letter sent late on Monday to EU leaders, including Tusk, UK Prime Minister Boris Johnson said the controversial Irish border backstop, included in the Brexit Withdrawal Agreement negotiated by former Prime Minister Theresa May, must be scrapped as it was "unviable" and "anti-democratic".
Johnson also said the backstop risked undermining the Northern Irish peace process.
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.”
He did not mention Johnson in the tweet but added, “Those against the backstop and not proposing realistic alternatives in fact support re-establishing a border. Even if they do not admit it.”
The exchange comes as pressure mounts on both sides to avoid the UK crashing out of the EU on 31 October without a deal.
Further reaction to the letter came from the European Commission which said Johnson's call to reopen the Withdrawal Agreement did not contain a "legally operational solution" to prevent a hard-Irish border.
"It does not set out what any alternative arrangements could be," a Commission spokeswoman said, and "recognises that there is no guarantee such arrangements would be in place by the end of the transitional period".
Johnson's four-page letter came ahead of meetings at the G7 summit in France later this week with German Chancellor Angela Merkel and French President Emmanuel Macron.
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 UK to unilaterally exit and no say for the people of Northern Ireland over the rules that would apply there.”
Johnson also warned that it risked "weakening the delicate balance" of the Good Friday peace agreement because unionist parties like the DUP are so unhappy with it.
“Those against the backstop and not proposing realistic alternatives in fact support re-establishing a border. Even if they do not admit it” Donald Tusk, EU Council President
The backstop, he argues, should be replaced with a commitment to put in place such arrangements as far as possible before the end of the transition period - currently the end of 2020 under former PM Theresa May's deal.
If they were not in place by the end of the transition period, Johnson said the UK was "ready to look constructively and flexibly at what commitments might help".
He wrote, "Time is very short. But the UK is ready to move quickly, and, given the degree of common ground already, I hope the EU will be ready to do likewise. I am equally confident that Parliament would be able to act rapidly if we were able to reach a satisfactory agreement which did not contain the backstop."
Elsewhere, US Senate Democratic leader Chuck Schumer has made it clear in a letter to the country’s Secretary of State Mike Pompeo that he will work with the Speaker of the House, Nancy Pelosi and members in both chambers of Congress to block any deal that threatens the Good Friday Agreement.
Schumer has warned President Donald Trump that they will vote against any trade deal with the UK if the Good Friday Agreement is damaged.
“Plainly stated, America should not be in the business of handing out a blank check that bankrupts the peace, security, self-determination and shared prosperity precipitated by the Good Friday Agreement.”
“Time is very short. But the UK is ready to move quickly, and, given the degree of common ground already, I hope the EU will be ready to do likewise” Boris Johnson, UK Prime Minister
Schumer also warned the Trump administration to stop “over-promising an unconditional and unrealistic” post-Brexit trade agreement with the UK.
Schumer’s letter comes in the wake of reports of a leaked top-secret British government document titled ‘Operation Yellowhammer’ that warns of expected violence and protests if a no-deal Brexit leads to the creation of a hard border between the Republic of Ireland and Northern Ireland.
Meanwhile, UK Labour leader Jeremy Corbyn has called on Johnson to publish all documents on the impact of a no-deal Brexit, after a leak at the weekend suggested there could be significant disruption to supplies of food and medicine.
Johnson’s government insisted the Operation Yellowhammer information was out of date and that Brexit planning had accelerated since he became Prime Minister.
Conservative Party chairman James Cleverly told the BBC on Tuesday: "What it is, it's an internal document to stimulate actions and behaviour of governments - it's not a prediction, it's not a future estimate of reality, it is a series of worst-case scenarios to be mitigated and avoided."