Theresa May has promised EU citizens living legally in the UK will be allowed to stay after Brexit.
The Prime Minister outlined what she called a "generous offer" to guarantee permanent "settled status" to three million EU nationals, speaking after an EU summit dinner in Brussels.
"The UK's position represents a fair and serious offer, one aimed at giving as much certainty as possible to citizens who have settled in the UK, building careers and lives and contributing so much to our society," she told the 27 remaining leaders of EU nations.
It would be dependent on the same rights being offered reciprocally to the one million UK citizens in other European countries, she said.
The plan, which will be published in full on Monday, guarantees permanent settled status for three million EU citizens already living in the UK, including rights to healthcare, education, benefits and pensions.
German Chancellor Angela Merkel said it was a "good start", but there were many issues still to be resolved.
The new legal arrangement would build on citizens' eligibility for permanent residence after five years.
Most people who have been in the UK for under five years will be given the chance to meet the five-year threshold for "settled status".
The deal also potentially offers it to some EU citizens yet to arrive, depending on the negotiation of a cut-off date with the EU.
The existing plan was to limit eligibility to those living here on the day Article 50 was triggered on 29 March.
The new plan offers the potential to change that date to the day when Britain is scheduled to leave the EU, in 2019.
Mrs May told EU leaders that no matter what was agreed on the cut-off date, there would be no "cliff edge" for any EU citizen lawfully resident in the UK on the actual day of Brexit.
Everyone would be given a two-year "grace period" to "regularise their status under new laws", she said.
The plan also scraps an onerous 85-page residency document that has led to much agony among EU citizens forced to supply boxes full of supporting documentation.
The Prime Minister promised "streamlined administration" that "used digital tools to register people in a light-touch way". This is another issue raised by the EU in its position paper on the same issue.
She said the rights would be guaranteed under UK law and in UK courts, not under European law as demanded by the EU position paper.
The proposal is not, however, clear on the extent to which rights of EU citizens are also passed on to descendants or family members, as asked for in the EU negotiating document.
The European leaders did not engage in a negotiation with Mrs May over the issue at the dinner.
President of the European Council Donald Tusk announced ahead of the dinner that "it must be clear the European Council is not a forum for Brexit negotiations".
Leaders merely took note of the Mrs May's offer.
The real negotiation will take place in the coming weeks in Brussels between Brexit Secretary David Davis and Michel Barnier, the EU's chief Brexit negotiator.