The European Council president said it was up to Theresa May’s government whether there was a “good deal, no deal or no Brexit”.
Meanwhile, the EU’s chief Brexit negotiator indicated that agreement on a free trade deal with Britain after it leaves the European Union will take years to complete.
Michel Barnier said the discussions would be very different from the first phase of the negotiations on the terms of Britain’s withdrawal and would entail “risks”.
His comments came after Ms May told MPs there could be no transition period after Britain leaves the EU unless there was agreement on a trade deal.
In a House of Commons statement, she said she remained confident a deal was possible following the latest EU summit last week in Brussels. Her remarks caused consternation among opposition MPs who warned the UK was heading for a “cliff-edge” break with the EU which businesses have been desperate to avoid.
Updating the European Parliament on last week’s Brussels summit, Mr Tusk stressed his obsession with the unity of the 27 members who will remain in the EU after the UK’s departure.
“Ahead of us is still the toughest stress test. If we fail it, the negotiations will end in our defeat,” he said.
“We must keep our unity regardless of the direction of the talks. The EU will be able to rise to every scenario as long as we are not divided.
“It is in fact up to London how this will end: With a good deal, no deal or no Brexit. But in each of these scenarios we will protect our common interest only by being together.”
European Commission chief Jean-Claude Juncker moved to reassure the UK that there was no “hostile” agenda from Brussels and a “no-deal” scenario was “not our working assumption”.
Mr Juncker told MEPs in Strasbourg: “The commission is not negotiating in a hostile mood. We want a deal. Those who don’t want a deal... they had no friends in the commission.”
Leaders of the other 27 EU states agreed on Friday to begin discussions among themselves on a possible transition period — prompting hopes in Downing St that they will agree to move to trade talks in December.
In an interview with France’s Les Echoes newspaper, Mr Barnier said agreement on a time-limited transition period after Britain leaves the bloc in March 2019 should be possible.
“If we reach an agreement on the orderly withdrawal of the United Kingdom, such a period, both short and framed, is possible,” he said.
“To my mind, it makes sense that it covers the financial period, so until 2020. It would leave us more time to prepare for the future relationship.”
However he warned that the negotiations would continue to be “difficult” and that agreeing the future relationship between the EU and the UK would take time.
“The two phases are difficult. The second will be very different and will last several years. It is truly unique because, instead of promoting regulatory convergence, it will aim to frame a difference. It will involve risks, including about its political ratification, making all the more necessary transparency around these topics.”
Ms May’s spokesman said the UK government believed it could agree a trade deal with the EU quickly.