In her speech in Florence, "May expressed a constructive spirit which is also the spirit of the European Union during this unique negotiation," Barnier said in a statement.

"The speech shows a willingness to move forward, as time is of the essence," he added.

Barnier, a former French foreign minister and EU commissioner, is to host his British counterpart David Davis in Brussels on Monday for a fourth round of negotiations, and he said he expected details from Britain at that meeting.

The EU institutions "look forward to the United Kingdom's negotiators explaining the concrete implications" of May's speech, he said.

May is hoping her speech will have unlocked the stalled talks in time for a meeting of EU leaders on October 19-20, when her 27 counterparts in the bloc will decide if negotiations can begin on trade, a dearly held wish of British leaders.

But the EU has insisted on "sufficient progress" in three key areas -- the rights of EU citizens in Britain, Northern Ireland's border and the exit bill -- before it will turn to post-Brexit arrangements.

In light of that demand, May promised to meet Britain's existing EU budget commitments until 2020 and outlined new legal guarantees for the rights of around three million EU nationals living in Britain.

Other EU reaction was also positive, including from the European Parliament's Brexit chief Guy Verhofstadt, usually one of Britain's harshest critics.

"Six months after the triggering of (the EU divorce process), it appears that the position of the UK is becoming more realistic," Verhofstadt said.

But he urged EU negotiators to stay "very cautious", in particular on the fate of EU workers in Britain.

The protection of their rights "must be absolute and beyond any doubt," he said.

The European Parliament, which will have a final vote on any Brexit deal when Britain leaves in March 2019, will vote a motion on the progress of the talks next month.