In her closely watched speech in Florence, "May has 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," added Barnier.

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.

In light of that meeting, Barnier said the EU institutions "look forward to the United Kingdom's negotiators explaining the concrete implications" of May's speech.

May is hoping her speech will be enough to unlock the talks in time for an EU leaders meeting on October 19-20, when her 27 counterparts will decide if talks can move on to trade.

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

In Florence, 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 the UK.

She also committed to maintaining Europe's security, saying in a direct pitch to EU leaders: "We want to be your strongest friend and partner as the EU and UK thrive side by side."