The Dutch prime minister, Mark Rutte, said there are "thousands of questions to ask" about May's proposals, and questioned why the British leader was laying them out with European Union leaders instead of with the Brexit negotiators.
Davis said Prime Minister May will also set out at an EU summit on Thursday her proposals for the rights of the three million EU nationals living in Britain, and one million Britons in the EU, with the British government to publish a detailed offer next Monday.
She added: "We want to conduct these negotiations in such a way that they take place in a good spirit, and we know that we want to continue working afterward with Britain".
No EU citizen now in Britain would be asked to leave on Brexit day, she said, while EU citizens living in Britain for more than five years will get "settled status".
Foreign Secretary Boris Johnson said he hoped leaders of the 27 other nations would match her "generous" proposals with similar offers to the one million British expats on the continent.
"For us it's not a question of generosity, it's a question of continuity and fairness", Stefaan De Rynck, a senior aide to chief EU Brexit negotiator Michel Barnier, said at a seminar in Brussels.
The fate of an estimated three million Europeans living in Britain and around one million Britons living elsewhere in the EU was thrown into doubt by Britain's vote to leave the bloc past year. The group would like to remind him that he and the United Kingdom government are also there to represent the 1.2 million United Kingdom citizens most directly impacted by Brexit - those who live in the European Union and have been in limbo for a year, waiting for talks to start.
The UK has accepted that the European Council will decide when "sufficient progress" has been made on these three baskets to allow talks on the EU/UK future relationship to begin.
Arrests at Capitol of health bill protesters
Mizuho Securities' director of research, Sheryl Skolnick, said in a research note, "Hospital stocks are up on this news today". McConnell's team put out a fact sheet this morning detailing their major changes to ObamaCare - or non-changes, I should say.
"When it comes to issues related to the border, the border between Northern Ireland and Ireland, it will be hard to determine the final shape of that until we know what the new trade arrangements are between the United Kingdom and the European Union".
She said: "I want to say clearly that, for me, shaping the future for the 27 takes priority over the negotiations with Great Britain over withdrawal".
"You may say I am a dreamer, but I am not the only one".
Tusk, who grew up in Communist Poland before the Soviet Union collapsed in 1991, said, however, that his personal history has taught him never to give up hope.
Newly-elected French President Emmanuel Macron and German Finance Minister Wolfgang Schaeuble both said last week that the "door was open" for Britain to remain in the EU.
Yet her aims have held - she wants a clean break from the bloc, leaving the lucrative single market and customs union and so reducing immigration into Britain and removing her country from the jurisdiction of EU courts. "Not for dreams and uncertainty #Brexit #Future of Europe", Michel tweeted.
European Union diplomats hope this first meeting, and a Brussels summit on Thursday and Friday where Theresa May will meet fellow European Union leaders, will improve the mood after some spiky exchanges.
"There is more that unites us than divides us", Mr Davis said, referring to the latest reported terror attack overnight in London and the loss of lives in forest fires in Portugal.
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