BRUSSELS - The European Union (EU) leaders have expressed doubts over the British Prime Minister Theresa May's fresh offer to protect EU citizens' rights on the second day of a summit on Friday.

The European Commission President Jean-Claude Juncker said "no" when asked whether he was any clearer about the kind of Brexit London wants.

"That is a first step but this step is not sufficient," he told reporters at his arrival of the summit.

May tried to reassure EU nationals in UK that their futures would be secure on Friday.

"No one will have to leave, we won't be seeing families split apart," she said before the summit.

May on Thursday made a "fair and serious offer" to her EU counterparts over the contentious issue of the future rights of EU citizens, saying those who arrived lawfully before Brexit would have the chance to build up the same rights to work, healthcare and benefits as British citizens.