British Prime Minister Theresa May arrives at the EU summit in Brussels. | FRANCOIS LENOIR

Theresa May said her offer to fellow EU leaders to guarantee the rights of their compatriots living in Britain after Brexit was "very fair and very serious" but her peers sounded sceptical, with Belgium's leader calling it "particularly vague".

"I want to reassure all those EU citizens who are in the UK, who have made their lives and homes in the UK, that no one will have to leave. We won't be seeing families split apart," May said on arrival for the second day of a regular European Union summit in Brussels this morning.

"Last night I was pleased to be able to set out what is a very fair and a very serious offer for EU citizens who are living in the United Kingdom," she said, adding that she would issue detailed proposals on Monday and seek reciprocal rights for about a million Britons living on the continent.

More detail was what most of the other 27 said they wanted, including German Chancellor Angela Merkel, who called it a «good start» but made clear that her focus was on the EU's future without Britain.

Belgian Prime Minister Charles Michel called it a «particularly vague proposal» and described it using a Flemish expression for a dubious gift.

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

In particular, the EU 27 want their citizens to be able to enforce their rights in Britain through the European Court of Justice, something May has flatly ruled out. They also dispute her attempt to limit those rights potentially to people already living in Britain before she triggered Brexit three months ago.

Given the floor for 10 minutes at the end of a Brussels summit dinner, 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.

May 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». Red tape for permanent residency would be cut and there would be a two-year grace period to avoid «cliff edge» misfortunes.