British Prime Minister Theresa May said on Friday the offer she had made on the rights of EU citizens to live in Britain after Brexit was very fair and very serious and that her government would set out more detailed proposals on Monday.

EU leaders greeted the offer made during a summit in Brussels late on Thursday with a degree of scepticism and said many questions remained.

"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 and the government will set out more detailed proposals on Monday," May told reporters before a second day of the EU summit on Friday.

"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," she continued, adding she also wanted similar guarantees for British people living elsewhere in the European Union.

Details of the arrangement would be part of the negotiation process, she added.