The prime minister’s other main meeting on today will see him set out face-to-face with Mr Tusk his absolute commitment to the 31 October deadline, even if that means leaving without a deal.
On Saturday, Mr Tusk said he hoped the prime minister would not go down in history as “Mr No Deal”.
But the prime minister shot back by suggesting that failure to reach a Brexit agreement would also reflect badly on Mr Tusk.
Mr Tusk warned he would no co-operate with a no-deal Brexit, an apparent sign the European Union would not be willing to create a series of side deals to manage the impact.
In comments as Mr Johnson prepared to board his plane to France, Mr Tusk said: “One thing I will not cooperate on is no deal. I still hope that Prime Minister Johnson will not like to go down in history as ‘Mr no deal’.
“We are willing to listen to ideas that are operational, realistic and acceptable to all member states including Ireland, if and when the UK government is ready to put them on the table.”
On the way to Biarritz, Mr Johnson gave his response, telling reporters: “I have made it absolutely clear I don’t want a no-deal Brexit.
“But I say to our friends in the EU if they don’t want a no-deal Brexit then we have got to get rid of the backstop from the treaty.
“If Donald Tusk doesn’t want to go down as ‘Mr no-deal Brexit’ then I hope that point will be borne in mind by him too.”
Mr Johnson said he expected talks on his alternative to the backstop “in the coming weeks”, with discussions “in great detail” .