Speaking ahead of Mr Johnson's arrival in France for the summit, Mr Tusk said he hoped the Prime Minister would not go down in history as "Mr no-deal".
But on the plane to Biarritz, Mr Johnson shot back at Mr Tusk ahead of their face-to-face talks, suggesting a failure to reach an agreement would also look bad on him.
The Prime Minister told 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 Tusk had used a press conference at the G7 to set out the European Union's position ahead of his talks with Mr Johnson, saying: "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."
The G7 summit this weekend will see Mr Johnson set out his plans for Brexit in talks with Mr Tusk, building on visits in recent days to the leaders of Germany and France.
Mr Johnson will also meet US president Donald Trump on Sunday, with Mr Johnson urging him to avoid escalating his dispute with Beijing after the Prime Minister landed in France at 2pm UK time.
Asked if he would be telling Mr Trump he should not escalate the trade war with China, Johnson said: "You bet."
Mr Johnson went on: "The three obsessions I have for the UK and the world at this G7 summit are clearly the state of global trade, I'm very worried about the way it's going, the growth of protectionism, of tariffs that we're seeing.
"The UK thrives mightily on being an open, outward-looking free trading nation."
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The G7 summit is also expected to discuss the destruction of the Amazon rainforest and other environmental issues.
Mr Johnson said: "We need to escalate here at the G7 the tragedy of what humanity is inflicting on the natural world."
Asked about agreeing trade deals with Brazil he said: "There are all sorts of people who will take any excuse at all to interfere with trade and to frustrate trade deals and I don't want to see that."