"We will not be intimidated by threats and I can assure you they simply will not work," Tusk told the European Parliament in Strasbourg, France.
"The claims, increasingly taking the form of threats, that no agreement will be good for the UK and bad for the EU, need to be addressed," Tusk said.
"I want to be clear that a no-deal scenario would be bad for everyone but above all for the UK."
British Prime Minister Theresa May said in January that she was ready to leave the EU without a deal on future relations if necessary.
"While I am sure a positive agreement can be reached -- I am equally clear that no deal for Britain is better than a bad deal for Britain," she said in a speech.
But former Polish premier Tusk, whose job as European Council head involves working to achieve consensus among the bloc's national leaders, said he remained optimistic that May would be sensible.
"Our goal is to have a smooth divorce and a good framework for the future. And it is good to know that Prime Minister Theresa May shares this view," he told MEPs.
'Door will remain open'
May's government has offered the British parliament a binding vote on the Brexit deal before Britain leaves in early 2019 -- but only once May has decided to accept it.
If she decides not to accept it, there is no deal to vote on.
Many MPs fear May will be pressured by the eurosceptic press and the Brexiteers into walking away from a deal that many of them would accept.
May conversely believes the EU could give Britain a worse deal if it thinks that MPs will accept it rather than crash out.
Tusk, who was re-elected last week despite the objections of his native Poland, said he would work to ensure Britain and the EU remained "close partners."
"The EU's door will always remain open to our UK friends," Tusk said.
The remaining 27 EU leaders will discuss the post-Brexit future at a summit in Rome on March 25 to mark the 60th anniversary of the bloc's founding treaty.