Speaking at a press conference at the G7 summit here, Tusk said that the EU is "willing to listen" to Johnson's ideas for Brexit if they are "realistic", but added that he would "not cooperate on no deal".
Since becoming Prime Minister, the former London Mayor has insisted the UK will leave the EU on October 31.
Tusk and the UK leader will meet on Sunday to discuss Brexit. The European Council President said that Johnson would be the third British Prime Minister (after David Cameron and Theresa May) he will meet since the UK voted to leave the EU in June 2016, the BBC reported.
"The EU has always been open to co-operation. One thing I will not co-operate on is a no deal. We are willing to listen to ideas that are operational, realistic and acceptable to all EU member states.
"I still hope Prime Minister Johnson will not like to go down in history as Mr No Deal," Tusk said.
The G7 summit a get-together of most of the leaders of the world's largest economies came with just over two months until Britain is scheduled to leave the EU.
Johnson wants to renegotiate the Irish backstop a key Brexit sticking point which is part of the withdrawal agreement and aims to prevent a hard border between Northern Ireland (which is part of the UK) and the Republic of Ireland (an EU member) after Brexit. The EU has consistently ruled this out.
Before arriving in Biarritz, the UK leader visited Berlin and Paris in search of a way out of the impasse between his government and European leaders on the issue of a backstop.
Tusk also had strong criticism for US President Donald Trump. Referring to the latter's increasing use of tariffs in trade relations, he said trade wars would lead to recession.
He took Trump to task for abandoning the 2015 nuclear deal with Iran, saying Washington's withdrawal had not brought about any "positive effect".
On the issue of the fires raging across the Amazon, Tusk pointed out that the EU's Mercosur free trade agreement with Brazil and three other South American countries, which has yet to be ratified, included safeguards for the environment.
"It is hard to imagine a harmonious process of ratification by the European countries as long as the Brazilian government allows for the destruction of the green lungs of the planet."
Ireland and France said they would not ratify the deal if Brazilian President Jair Bolsonaro did not change his environmental policies.
( With inputs from IANS )