Video report by ITV News Europe Editor James Mates
"A no-deal would be dangerous for Britain and the European Union," Jean-Claude Juncker, President of the European Commission, has told the EU summit in Brussels.
Speaking alongside the European Council president Donald Tusk he said: "I'm convinced that under the leadership of Donald, we'll find a deal.
"My working assumption is not that we will have a no-deal, a no-deal would be dangerous for Britain and the European Union."
His comments follow Theresa May's suggestion that the idea of extending the Brexit transition period "for a matter of months" had been considered.
However, Mr Tusk said the possibility of extending the transition period was not discussed at the meeting of the EU 27.
Addressing the summit, Theresa May said there was a "lot of hard work ahead" and "difficult moments" as negotiators enter the final stage of talks.
"Last night I updated my fellow leaders on the good progress that has been made on the Brexit negotiations," she said.
"On the withdrawal agreement there are a few but considerable outstanding issues in relation to the northern Irish backstop."
However, she said she is "convinced that we will secure a good deal that is in the interest of the UK and the EU."
Mr Tusk said that after speaking to Mrs May on Wednesday the EU 27 confirmed they wanted to continue talks in a "positive spirit".
"In her Florence speech in September 2017, Prime Minister May proposed a transition period of around two years and the EU accepted this proposal unanimously," he said.
"Therefore, if the UK decided that an extension of the transition period would be helpful to reach a deal, I am sure that the leaders would be ready to consider it positively."
Earlier in the day German Chancellor Angela Merkel said they still needed to find a solution to the Irish border issue.
"All of the 27 said that we wish to bring about a solution, one that clearly expresses the fact that Britain is no longer a member of the EU, but also expresses what we all want politically speaking - namely that we establish a good relationship with Britain for the future," she told an end-of-summit news conference in Brussels.
"As long as we don't have a satisfactory solution we cannot really explain in a satisfactory way how this is to come about but I think where there is a will there is a way. That is usually the way.
"We agreed that once there is sufficient progress we will meet again at any point in time that is convenient, but right now we cannot safely say when such a meeting should take place."