European Commission President Jean-Claude Juncker said the proposals were "a first step, but not sufficient".
Merkel said there was still a lot of work ahead, including the question of a British financial settlement as well as how to manage the border between Ireland and Northern Ireland.
Those arriving up until the point of departure would have a "grace period" - expected to be two years - to build up the same "UK settled status" and the system would also be streamlined, doing away with an 85-page permanent residency application form which has attracted complaints, May said in a clear attempt to sweeten Britain's offering for Brexit.
Those with less than five years' residence before the cut-off date will be allowed to stay until they have clocked up five years' residence, and then apply for settled status.
But the plan, unveiled on the eve of the first anniversary of Britain's Brexit referendum, has been heavily criticized.
Arriving at the European Council summit in Brussels, the Prime Minister reaffirmed her intention that the future of the 3.2 million EU nationals in the United Kingdom and 1.2 million United Kingdom citizens in the EU should be one of the first issues to be resolved. "By doing so she is treating British people living in Europe, the same", he said.
Earlier, Tusk had channelled John Lennon's "Imagine" as he said he hoped Brexit could be reversed - though others immediately poured cold water on the idea. "For me the shaping of the future of the 27 is a priority coming before the issue of the negotiations with Britain on the exit", she said.
Cindy Now a Tropical Depression
With Cindy now inland, the tropical Atlantic Ocean basin is quiet - after the unusual flurry of mid-June storm activity. Carroll said the Triangle area may not see rains from Cindy's aftermath until Friday night or early Saturday.
Other leaders took up the late Beatles theme, though were clear they though a U-turn on Brexit highly improbable. The EU citizens, under the special category of "settled status", would get the same rights to work, pensions, NHS care and other public services as British citizens, which they will maintain for life.
Discord over whether the exit process could still be reversed surfaced at the summit in Brussels as British Prime Minister Theresa May was preparing to brief the 27 European Union other leaders on the Brexit negotiations that started this week.
There are categories of people whose status may remain unclear, such as children, carers, students and Irish citizens.
In other business, the European Council made a decision to finalize works on a new border information sharing system this year in a bid to protect residents against terrorism, according to a statement by the bloc at the end of the first day of the high-level summit.
German Chancellor Angela Merkel gave a cautious welcome yesterday to British Prime Minister Theresa May's offer on European Union citizens' rights post-Brexit, saying it was a "good start" but more needed to be done. German Chancellor Angela Merkel called them "a good start".
While there was a cautious welcome from Merkel, others were less forthcoming.
Dutch Prime Minister Mark Rutte said that as an Anglophile, "I hate Brexit from every angle". Using a Flemish phrase to describe a dubious gift, he said: "We don't want a cat in the bag". "We want this negotiation to take place in a good spirit". "I arrived here before 2014. but [the proposals] open more questions than they answer. There is a long, long way to go for negotiations", Kern said.
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