On Wednesday, the Prime Minister set out her priorities for Brexit talks in a letter which triggered Article 50, in which she said divorce talks and free trade talks should take place at the same time.
Speaking in Malta on Friday morning, Tusk admitted that Brexit talks would be hard and perhaps even confrontational but stressed that the European Union does not seek to punish Britain for its decision to leave.
May, who officially triggered two years of Brexit negotiations Wednesday, has repeatedly said she wants to guarantee the rights of some 3 million European Union citizens resident in Britain, but that it's contingent on a reciprocal promise by the EU's 27 other governments for more than 1 million Britons resident in their countries.
British Prime Minister Theresa May published columns in seven European papers on Thursday to stress that a Brexit deal was "in all our interests", striking a conciliatory tone before negotiations begin.
However, this was immediately rejected by both German chancellor Angela Merkel and the French president Francois Hollande.
On security cooperation, Tusk said that especially after the terrorist attack in London it is clear security and terrorism are a common problem and security cooperation will not be used as a bargaining chip. He said there would be "no punitive approach, Brexit is punitive enough".
The EU's chief negotiator, France's Michel Barnier, is expected to get the green light to start talks with Britain on May 22, an EU official said.
"As our closest friend and neighbour, we hope after our departure to establish a close and special relationship with all the countries in the European Union".More news: WWE flexes sports entertainment muscle at WrestleMania
Britain's EU ambassador delivered a letter from May to European Council President Donald Tusk, confirming the plan to leave and formally launching the process, nine months after Britons voted in a referendum on June 23.
A spokesman for May said the guidelines showed a constructive approach.
Announcing the details of the white paper, Brexit minister David Davis said there would be three key elements: to repeal the European Communities Act; to convert any existing EU law into United Kingdom law; and to give parliament powers to create secondary legislation to enable corrections to any laws that would no longer be appropriate once we have left the EU.
'It would be to the detriment of us all if unnecessary barriers to trade were erected, ' she said.
But May's warning in the letter that failure to clinch a deal on trade would affect Britain's cooperation on terrorism and security still rankled with many.
Foreign Secretary Boris Johnson responded: "I think we really are moving forward now".
European Council President Tusk: The EU does not want to punish Britain for Brexit.
Article 50 of the Lisbon Treaty gives both sides two years to reach agreement so, unless the United Kingdom and the 27 remaining European Union member states agree to extend the deadline for talks, the United Kingdom will leave on 29 March 2019.