- Video report by ITV News Europe editor James Mates
Reports of a Brexit stalemate have been "exaggerated", European Council President Donald Tusk has said - adding that leaders were approaching negotiations "positively and constructively".
The EU's chief negotiator Michel Barnier has described the talks as deadlocked, sparking fears over the progress of talks.
But speaking at a press conference on Friday, Mr Tusk said: "While progress has not been sufficient, it doesn't mean there has been no progress at all.
"The negotiations go on and we will continue to approach them positively and constructively."
They are expected to move to the second phase of talks in December, he added.
He also insisted he was not at odds with Mr Barnier, saying: "Michel Barnier is responsible for the negotiations, I am more responsible, first of all for our unity, but also for a good atmosphere and positive mood. This is the only difference."
German Chancellor Angela Merkel gave a similarly upbeat assessment of the talks, saying they were making progress "step by step".
"I have no doubt that if we are all in clear minds ... We are going to achieve a good outcome," she said.
"As far as I am concerned, I don't hear any reason to believe that we are not going to be successful."
Meanwhile, European Commission president Jean-Claude Juncker said he too hoped it would be possible to reach a "fair deal" with Britain.
He said that, prior to the summit, no-one on the UK side had explained the consequences if they failed to reach an agreement.
"I hate the 'no-deal' scenario. I don't know what that means," he said. "I am not in favour of 'no deal'. I want to have a fair deal with Britain."
EU leaders will continue discussions on Britain's exit at the summit but Mrs May will not be present.
The progress in discussions paves the way for the possible start of formal talks on the future trade relationship between the UK and EU in December.
Until then they will continue to focus on the "divorce" issues of citizens' rights, the Irish border and Britain's financial settlement.
As for the UK Prime Minister, she said she remained "ambitious and positive" for negotiations on the UK's withdrawal from the European Union.
However, she added: "I know we still have some way to go. Both sides have approached these talks with professionalism and a constructive spirit and we should recognise what has been achieved to date."
Watch Theresa May's full speech:
Mrs May also said the two sides were within "touching distance" on a deal regarding the rights of EU citizens living in the UK and British citizens in the EU.
"EU citizens have made a huge contribution to our country and let me be clear that whatever happens we want them and their families to stay."
Mrs May also insisted that while there are a "small number of issues" that remain on citizens' rights she is confident of a deal.
The prime minister also said she had outlined her vision for a new "deep and special" partnership with the EU after Brexit to leaders over dinner on Thursday.
"A partnership based on the same set of fundamental beliefs, in not just democracy and rule of law but also free trade, rigorous and fair competition, stronger consumer rights and high regulatory standards," she said.
The 27 remaining member states are seeking more clarity from the UK about the size of its divorce bill before giving the go-ahead for trade talks to get under way.
The offer made by Mrs May in Italy is believed to amount to around 20 billion euros (£18 billion), while Brussels is understood to be seeking something closer to 60 billion euros.
Asked whether she would deliver further details on the divorce bill in time to ensure a breakthrough at the next summit, Mrs May said: "On the financial issue, we will be going line by line through those commitments."
She added: "The full and final settlement will come as part of the final agreement that we are getting in relation to the future partnership and I think that's absolutely right, I think that can only be done in that particular context."