May will attend a European Council summit Thursday to speak to her European counterparts about her plans for the 3 million EU nationals living in Britain - an issue she says is her first priority for early agreement in the Brexit talks.
The European Union said after a first day of talks on Britain's exit from the 28-member bloc that the clock was ticking on negotiations, but British Brexit minister David Davis said he was optimistic they would yield a swift and good outcome.
Brussels has been dismissive of May's call for sweeping and quick guarantees for expats, including over a million Britons on the continent, and says only detailed legal texts can reassure and take account of complex, multinational family situations.
The UK government has been forced in to a major climbdown on the first day of Brexit negotiations after being forced to accept the EU's timetable for talks.
Given that a disorderly departure from the European Union would have greater impact on the British economy than on Europe's, officials have warned that Brussels would have the upper hand in several aspects of the talks because of the limited time available to conclude a comprehensive exit deal.
British Prime Minister Theresa May speaks with the media as she arrives for an European Union summit at the Europa building in Brussels on Thursday, June 22, 2017.
After ten months of planning, Davis will meet with the EU's Chief Negotiator Michel Barnier to agree the structure of the negotiations ahead, so officials have a framework within which to discuss substantive issues.
Time is pressing. After the June 23, 2016, referendum to leave the bloc, the other 27 nations wanted to start the exit talks as soon as possible so they could work on their own future but Britain long seemed dazed by its own momentous move.More news: Final farewell for U.S. student detained by North Korea
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"The PM said the UK's position represented a fair and serious offer - and one aimed at giving as much certainty as possible to citizens who have settled in the United Kingdom, building careers and lives, and contributing so much to our society". He said: "I am not a dreamer".
Barnier said there was agreement that the negotiators would first look at citizen's rights, the outstanding bill Britain must pay for previous European Union commitments and the Irish border issue. Austrian Foreign Minister Sebastian Kurz said: "If we don't succeed, both sides will lose". We must lift the uncertainty caused by Brexit.
But Merkel said that "for me, shaping the future of the 27 member states has priority over the question of the negotiations with Britain on its exit".
Macron identified no countries, but European Union leaders are criticizing Poland and Hungary in particular for their refusal to accept migrants.
The negotiations kick off in Brussels on Monday with Britain under pressure for stalling the talks and entering the negotiations without a working parliamentary majority fully in place.
Billionaire currency trader George Soros has said Britain is approaching a tipping point that could see the economy slow to such an extent that Brexit might even be reversed, Reuters reported on Tuesday.
Mr Murray said it was "pie in the sky" to suggest that a trade and customs deal would secure the same access for to the European single market as EU membership. "Never before have I had such a strong belief that things are going in a better direction", he said.
Two foiled terrorist attacks this week alone put renewed focus on EU-wide efforts to improve counter-terrorism measures.