Mr Tusk said he hoped the Prime Minister would not go down in history as "Mr no deal" ahead of their face-to-face talks at the G7 summit in Biarritz on Sunday.
But speaking on the plane to Biarritz, the Prime Minister shot back by suggesting that failure to reach a Brexit agreement would also reflect badly on Mr Tusk.
The Prime Minister said: "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 Tusk had used a press conference at the G7 to set out the European Union's position ahead of his talks with Mr Johnson.
He said: "He will be the third British Conservative prime minister with whom I will discuss Brexit.
"The EU was always open to co-operation when David Cameron wanted to avoid Brexit, when Theresa May wanted to avoid a no-deal Brexit and we will also be ready now to hold serious talks with Prime Minister Johnson.
"One thing I will not co-operate on is no deal. I still hope that Prime Minster 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."