May and Tusk also discussed the upcoming Brexit negotiations, which will begin in earnest next month.
Theresa May has used her first meeting with European Council president Donald Tusk since triggering Article 50 to warn EU leaders that the sovereignty of Gibraltar is not up for negotiation in Brexit talks.
He also stressed that parallel talks on future EU-UK relationship are not possible until the uncertainties linked to the past are sorted out satisfactorily.
"You will set the tone for Britain", the bloc's Brexit negotiator Michel Barnier told MEPs just before the vote.
European Union chief negotiator Michel Barnier called parallel talks on Britain's exit from the European Union and a future trade relationship "a very risky approach" that he is bent on avoiding.
When asked if she would rule out free movement during any transition period after Britain leaves the European Union in two years' time, the Prime Minister said she would call it an "implementation period" instead.
"There's obviously a legal situation in terms of how the European Union can conduct trade negotiations".
She said there would be an "implementation" phase once a deal has been struck, for businesses and the Government to adjust to the new rules.
Nigel Farage, former UKIP leader and still its leader in the European Parliament, called the EU negotiating position "a form of ransom demand".
The Obamas yachting with Springsteen, Oprah and Tom Hanks
According to Vulture , Barack is working on his White House memoir , while Michelle readies a book project of her own. During this time, the Obamas were at a nearby exclusive resort: The Brando, on the private island of Tetiaroa.
The timing of the trade talks is likely to be high on the agenda for discussion.
The Parliament's Brexit coordinator, Mr Guy Verhofstadt, said it was perhaps best that there was never much positive passion in the cross-Channel relationship.
The leader of the EPP group of centre-right MEPs, Germany's Manfred Weber, told the Parliament that the United Kingdom could not simply pick and choose areas such as security, scientific collaboration and free trade where it wanted to co-operate with the remaining 27 member states.
But no reference to Gibraltar was contained in the adopted resolution.
The territory's Chief Minister Fabian Picardo said he had spoken repeatedly in recent days to Britain's Brexit minister David Davis, who reassured him he would "not allow himself to be bullied into accepting inferior treatment for Gibraltar". "Gibraltar is clearly a deal-breaker on current terms".
The row came as the Parliament heard a string of senior MEPs insist that Britain can not enjoy "the same or better conditions" in its relations with the European Union as full member states after Brexit.
The Parliament erupted in jeers at Mr Farage, forcing President Antonio Tajani to stop him in his tracks.
After he was chastised by the Italian chair of the European Parliament, Farage said: "I do understand national sensitivities".
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