"My first impression is that the UK's offer is below our expectations and that it risks worsening the situation of citizens", he told reporters.
One year after Britain voted to leave in the June 23 referendum, May promised that nobody would be forced to leave after Brexit, offering permanent rights over healthcare, education, welfare and pensions to Europeans who arrive before a cut-off date.
The cut-off date for entitlement to apply is yet to be set, but it will come somewhere between the day Britain activated Article 50 (29 March 2017) and the day Brexit takes effect (29 March 2019).
But her proposal on Thursday was criticised for not being clear enough.
"You could say that this is actually something that should be taken for granted", Sigmar Gabriel said after talks with his French counterpart in Paris.
May however defended the proposal.
Even though the Prime Minister emphasised she did not want to break up families or deport anyone now living in Britain, EU leaders withheld judgment on the proposal, choosing to wait for the release of the full plan next Monday.
Others would be allowed to stay until they reach the five-year threshold for "settled status".
"I think that's a very serious offer", she added.
She said the contentious issue of the jurisdiction of the European Court of Justice in guaranteeing such rights was a matter for the negotiations, though she insisted the rights would be protected by the "highly respected United Kingdom courts".
First woman leads Buckingham Palace Changing of the Guard ceremony
Princess Patricia had special links with Buckingham Palace, the place of her birth on March 17 1886. Captain Couto said: 'I'm just focusing on doing my job as best I can and staying humble.
Belgian Prime Minister Charles Michel was among the most sceptical, wary of getting a nasty "cat-in-the-bag" surprise. "The rights of European citizens should be guaranteed in the long term".
Mrs May again set her face against the idea that the European Court of Justice (ECJ) could enforce EU citizens' rights, an idea which is part of the formal proposal already tabled by Brussels.
German Chancellor Angela Merkel said it was a good beginning but does not represent a breakthrough.
She added: "But there are still many, many other questions linked to the exit, including on finances and the relationship with Ireland".
May had previously refused to guarantee the rights of Europeans until the futures of one million British expatriates living in the rest of the EU were also secured, and she said in Brussels that her proposal depended on a reciprocal deal.
The Black Country and Staffordshire voted overwhelmingly in favour of Brexit in the European Union referendum, with high immigration to the region thought to be one of the key issues behind the high support for the Leave campaign.
Juncker was asked if he knew what form of Brexit the government in London was now seeking, to which he replied: "No".
"We've made what I believe is a very serious, a very fair offer which will give reassurance and confidence to European Union citizens living in the United Kingdom about their future", Mrs May told reporters in Brussels yesterday.
"But from our point of view, these will be enforced, they will be enshrined in United Kingdom law, they will be enforced through the highly respected United Kingdom courts and of course if this is an aspect of the withdrawal treaty then it will be enshrined in worldwide law as well".
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