Theresa May's promise aims at giving a degree of certainty to EU citizens who have settled in the UK, but many of her peers remain sceptical and demand more details.
Theresa May offered fellow EU leaders "a fair and serious offer" on Thursday for compatriots living in Britain after Brexit, a British official said.
Given the floor for 10 minutes at the end of a Brussels summit dinner, her first since she launched the two-year withdrawal process in March, May outlined five principles, notably that no EU citizen resident in Britain at a cut-off date would be deported. There are roughly 3 million living there now.
Promising details on Monday, May also said those EU citizens who had lived in Britain for five years could stay for life.
Those there for less would be allowed to stay until they reach the five-year threshold for "settled status," she added.
Red tape for permanent residency would be cut there would be a two-year grace period to avoid "cliff edge" misfortunes.
Merkel pleased but not entirely convinced
German Chancellor Angela Merkel, who earlier said she wanted "far-reaching guarantees," described giving full rights to those in Britain for five years as "a good start" but said many questions remained.
Austrian Chancellor Christian Kern said it was "a first good step" 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," Kern said.
Other leaders offered few details on their reservations.
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.
EU agencies to leave London
Leaders had agreed with summit chair Donald Tusk not to open discussions with May and she left immediately afterwards, leaving the other 27 to discuss other Brexit issues without her.
They were briefed by Michel Barnier, who launched the Brexit negotiations for them on Monday, and discussed the move of two EU agencies from London after Britain quits.
Merkel and French President Emmanuel Macron, among others, had made clear that they did not want to be drawn into Brexit talks and wanted to focus on the future of the EU minus Britain.
May seemed keen to calm the mood with the continentals after weeks of sniping during her election campaign, stressing that London wanted a "special and deep partnership" with its friends and allies in Europe.
Merkel also expressed a desire for constructive talks with Britain, but made clear that the EU's priority now was its own future: "We will conduct these talks in a good spirit," she said. "But the clear focus has to be on the future of the 27."
France's new president Emmanuel Macron spoke of working with Germany to revive European integration and did not refer at all to Britain during his remarks before talks got under way.