"We will continue to play our part in ensuring that Europe remains strong and prosperous and able to lead in the world", she writes in the "Irish Times", a day after formally launching the process of the UK's exit from the EU.
"Once, and only once we have achieved sufficient progress on the withdrawal, can we discuss the framework for our future relationship", he told reporters in Malta - a compromise between European Union hardliners who want no trade talks until the full Brexit deal is agreed and British calls for an immediate start.
The EU has proclaimed its unity on Brexit, even as it reels from Britain's intention to become the first member state to leave in the bloc's 60-year history.
Tusk said he had hurried to present the guidelines swiftly because the negotiations would be conducted under a tight timetable: "The Treaty gives us only two years", he said, indicating that there was not much appetite to extend the period.
The negotiations will be among the most complex global talks ever undertaken.
Let me conclude by saying that the talks which are about to start will be hard, complex and sometimes even confrontational.
After these main issues are taken care of, Tusk said he shared the U.K.'s desire to establish a close partnership in their future relationship.
In a clear warning to the United Kingdom not to attempt to gain advantage by using divide-and-rule tactics to cut special deals with national capitals, the guidelines state that member states will not negotiate individually with the United Kingdom but through a fixed point of reference - the EU's chief Brexit negotiator Michel Barnier.
Once the first phase is cleared, the next phase of negotiations is set to scope out an understanding of a framework for the future UK-EU relationship.
However, the Prime Minister has stressed "now is not the time" to be talking about a Scottish referendum as the United Kingdom tackles Brexit, indicating that such a move was unlikely until after Britain's withdrawal from the European Union on 29 March 2019.
Prime Minister Theresa May's Conservative Government set out its plans on Thursday for a "Great Repeal Bill" to incorporate EU law into British law and "end the supremacy of EU lawmakers" after Britain leaves the European Union.
People must not be used as bargaining chips by any side, and this issue should be settled as quickly as possible, said Muscat, whose country holds the rotating European Union presidency from January to June this year.
"To enable these laws to function properly on exit the government needs to undertake a program of legislation to correct the statute book while Article 50 negotiations take place", said Davis.
He jibed that there would be no extra punishment for Britain because "Brexit in itself is already punitive enough". The leaders, who will meet at a summit on April 29, must approve the proposals.
The Leave Means Leave campaign said Mrs May should "walk away from the table" if Brussels refuses to talk about trade alongside the divorce settlement.
Analysts said the tone of Wednesday's historic announcement and the EU's initial reaction was largely conciliatory except for the warning on security.