During her first EU summit since she became PM following the Brexit vote and on her 100th day in office, May held meetings with her EU colleagues including European Commission President Jean-Claude Juncker.
"I recognise the scale of the challenge ahead, I am sure there will be difficult moments, it [Brexit] will require some give and take," she told reporters.
"But I firmly believe that if we approach this in a constructive spirit, as I am, then we can deliver a smooth departure and build a powerful new relationship that works both for the UK and for the countries of the EU, looking for opportunities, not problems," she said.
"The UK will continue to face similar challenges to our European neighbours, we will continue to share the same values, so I want a mature, cooperative relationship with our European partners," she said.
She had arrived for the two-day summit yesterday, stressing that the UK was leaving the EU but would "continue to play a full role" until then and be a "strong and dependable" partner after that.
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