Lawyers say that without such a step, the United Kingdom would end up in a legal limbo when it leaves the EU after applying European law for more than 40 years.
The move flies in the face of Ms May's call for talks on withdrawal and future trade terms to start at the same time, but does leave open the possibility of them eventually taking place in tandem as long as divorce talks advance.
President of the European Council Donald Tusk confirmed delivery of the letter on social media.
Resolving the status of British and other European citizens living in each other's countries will be an early priority. The president of the European Parliament said what Britain owes must be finalized before trade deals could be discussed. He added that "there is no one who wants to use citizens as hostages in this, no one". After it departs, Britain will continue to be Europe's second-biggest economy, so a constructive deal is needed.
"It will provide clarity and certainty for businesses, workers and consumers across the United Kingdom on the day we leave the EU".
The EU's draft guidelines for Brexit are uncompromising and firm.
Today my task is to propose the draft negotiating guidelines on Brexit to the 27 European Union leaders.
Tusk said the talks would be hard and sometimes confrontational, saying it was his "first divorce and I hope the last one".
A United Kingdom government spokesman said: "These are draft guidelines and we look forward to beginning negotiations once they have been formally agreed by the 27 member states".
She also underlined worldwide cooperation with Italy in La Repubblica and referred to an estimated 600,000 Italian nationals living in Britain and three million British tourists who visit Italy every year.
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"We really are moving forward now. There's a lot of good will, willingness to achieve what the Prime Minister has said she wants to achieve", he said.
Among the criticisms aimed at May, the EU's chief Brexit negotiator, Guy Verhofstadt, lablled the tactic "blackmail", and warned that security should not be used as a bargaining chip.
The reference to "sufficient progress" being required in the divorce talks before moving on to trade may be interpreted in London as a welcome signal that the Brexit deal does not have to be finalised before negotiations on future relations begin. Tusk had 48 hours to respond to the notification of withdrawal.
'We already miss you, ' Tusk said.
Tusk put guidelines on Britain's exit to the remaining 27 European Union members Friday.
The head of the rotating European Union presidency, Maltese Prime Minister Joseph Muscat, insisted the negotiations "will not be a war".
Ireland's unique Brexit concerns will be flagged in the EU's draft blueprint for negotiations with Britain, to be circulated on Friday to member states.
Speaking after the release of the Council's draft negotiating guidelines Friday morning he adopted an uncompromising stance on the U.K.'s preference to hold discussions on the divorce and future trade in parallel.
Joseph Muscat also said Northern Ireland would get "serious and special" consideration.