London (CNN) British Prime Minister Theresa May has come under attack from a host of European leaders over her plans for EU nationals living in the UK after Brexit.

May, who revealed her proposals to leaders on Thursday, was forced to defend her stance as Europe's politicians left the PM with little doubt of their disappointment.

Jean-Claude Juncker, head of the European Commission, said the offer was "not sufficient," while Donald Tusk, President of the European Council, said it was "below our expectations."

May told European leaders that none of the three million EU citizens currently living in Britain would have to leave in the wake of the country's departure from the bloc, and dismissed the prospect that families could be split up.

According to the British government's plans , a new "settled status" would allow EU nationals who have lived in the UK for five years to remain and enjoy access to healthcare, education and other benefits.

May added that those who had spent a shorter time in the UK would be permitted to remain until they reach the five-year point. Others who arrive after an as-yet-undisclosed cut-off date will benefit from a "grace period," expected to last two years.

The proposal is dependent on British nationals living in EU states being offered a reciprocal deal.

Speaking at the end of the European Council Summit in Brussels on Friday, Tusk said he was unimpressed with May's offer.

"My first impression is that the UK's offer is below our expectations, and it risks worsening the situation of citizens," Tusk said. "But it will be for our negotiating team to analyze the offer line-by-line once we receive it on paper."

'Cat in a bag'

May described the offer as "fair and serious," but some of her colleagues took a different view.

Dutch Prime Minister Mark Rutte said there were "thousands of questions to ask" after listening to May's presentation over a working dinner on Thursday evening.

Belgian Prime Minister Charles Michel labeled it a "particularly vague proposal."

"We don't want a cat in the bag," he said. "We want the rights of EU citizens to be permanently guaranteed," he said.

Austrian Chancellor Christian Kern was guarded in his assessment of May's plan.

"It is a first good step which we appreciate," he said. "(But) many details are left open. A lot of European citizens are concerned and not covered by May's proposal. There is a long, long way to go for negotiations."

Guy Verhofstadt, the European Parliament's Brexit coordinator, was also critical of May's stance.

Mays "generous offer" does not fully guarantee the rights of EU citizens living in the UK (1/2) — Guy Verhofstadt (@GuyVerhofstadt) June 23, 2017

"May's 'generous offer' does not fully guarantee the rights of EU citizens living in the UK," he wrote on Twitter. "Hopefully the UK position paper, expected on Monday, will deliver what we are looking for."

'Unacceptable'

The plan, unveiled on the eve of the first anniversary of Britain's Brexit referendum, has also been heavily criticized in Britain.

Mayor of London Sadiq Khan labeled the government's stance "unacceptable."

"It has taken a full year since the EU referendum for the Prime Minister to come up with a plan which does not come close to fully guaranteeing the rights of EU nationals living in the UK," Khan said in a statement.

"Her proposal doesn't go anywhere near giving the three million EU citizens living in Britain -- one million of whom are Londoners -- the certainty they need to make long-term plans for themselves or their families."

The PM's plan doesn't come close to fully guaranteeing the rights of the 3 million EU nationals living in the UK. https://t.co/uAhHxOegkv pic.twitter.com/s8Qm2Rmr8F — Sadiq Khan (@SadiqKhan) June 23, 2017

"It is unacceptable for the Prime Minister to be treating EU citizens living here and contributing to our economy and society as bargaining chips. By doing so she is treating British people living in Europe, the same," he said.

He urged May to "abandon her extreme, Hard Brexit approach, guarantee the rights of EU nationals in our country and secure a deal that protects jobs, investment and prosperity across the county."

Friday marks a year since Britain voted to leave the European Union -- but negotiations over the terms of the departure only began last week, and much remains unclear as to the future relationship between the two.

How will it work?

May, whose position is weakened after her party's majority was wiped out in the general election earlier this month, made her presentation to the leaders of the other 27 EU nations on Thursday evening.

The Prime Minister told colleagues:

EU nationals who have lived in the UK for five years by the cut-off date will be able to gain "settled status."

The new status will enable them to remain in the country and enjoy the same rights as British citizens in terms of access to healthcare, education, welfare and pensions.

EU nationals who have lived in the UK for less than five years will be allowed to remain until they have reached the five-year point.

Those who arrive in the UK after the cut-off date but before the country leaves the EU will be given a "grace period," expected to be two years.

That "grace period" will allow EU nationals to clarify their immigration status and ensure they are able to seek settled status.

While a cut-off date is yet to be set, Britain has already said it plans to leave the EU on March 29, 2019.

Further details are expected to be released on Monday when the Government publishes a paper on the subject -- it may offer some clarification as to whether those with settled status will be allowed to bring children or spouses into the country.

It may also address whether there will be any further conditions apart from the length of residency.

'Good start'

German Chancellor Angela Merkel called May's offer a "good start" but warned there were still many other obstacles to overcome before Britain's departure from the EU.

"Theresa May made clear to us today that EU citizens that have been in Britain for five years will retain their full rights. That is a good start," Merkel told reporters Thursday.

"But there are still many many other questions linked to the exit, including on finances and the relationship with Ireland. So we have a lot to do until (the next EU summit in) October."

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May also told a news conference that several leaders she had spoken to had reacted positively to the offer on EU citizens.

"I want all those EU citizens who are in the UK, who have made their lives and homes in our country, to know that no-one will have to leave," she said.

"We won't be seeing families split apart, people will be able to go on living their lives as before. This is a fair and serious offer," she insisted.

"It gives those three million EU citizens in the UK certainty about the future of their lives and we want the same certainty for the more than one million UK citizens who are living in the European Union."

Point of contention

One area which is bound to cause controversy is the EU's desire to see the European Court of Justice enforcing the rights of EU citizens within the UK.

That is a demand which May is unwilling to accept. She told fellow leaders: "The commitment that we make to EU citizens will be enshrined in UK law, and will be enforced through our highly respected courts."

Arriving for the second day of the summit, May said there are details of the arrangement which remain open to negotiation.

"This is a fair and serious offer," she said. "I want to give those EU citizens in the UK certainty about the future of their lives, but I also want to see that certainty given to UK citizens who are living in the EU."