Securing a Brexit deal for both sides will require "courage, trust and leadership", Theresa May told European leaders ahead of a dinner in Brussels on Wednesday.
More details have emerged from her 20-minute address, which European Parliament President Antionio Tajani said did not contain “anything substantially new in terms of content”.
Urging the European figureheads to coordinate “creative” solutions to their issues, she said: "We have shown we can do difficult deals together constructively.
"I remain confident of a good outcome.
"The last stage will need courage, trust and leadership on both sides."
She also stressed that she believed significant progress had been made in many areas of the negotiations.
The speech came ahead of the other leaders eating together, while Mrs May left for a fish dinner at the UK ambassador's residence.
The EU leaders were left to discuss Brexit in her absence and dined on pan-fried mushrooms, turbot cooked in wheat beer and a trio of fig, pear and grape sorbets.
In the wake of her speech, Mr Tajani said: "The tone was more relaxed than in Salzburg, undoubtedly.
"There was a message of goodwill and readiness to reach an agreement.”
Ahead of her main talk, Mrs May held separate meetings with French President Emmanuel Macron, Irish Tiaoseach Leo Varadkar, European Commission President Jean-Claude Juncker and European Council President Donald Tusk.
British officials characterised these as "constructive and serious conversations".
The EU's chief negotiator for Brexit, Michel Barnier, said "much more time" was needed to bridge differences between the two sides.
He promised to "continue the work in the next weeks calmly and patiently".
A number of EU leaders voiced willingness to work for an orderly UK withdrawal.
However, some noted their countries were beginning to prepare for a possible no deal Brexit scenario.
Theresa May, speaking as she arrived at the European Council building earlier on Wednesday, said: "The teams have been working very hard to ensure we can address these issues. We have solved most of the issues in the withdrawal agreement. There is still the question of the Northern Irish backstop.
"But I believe everybody around the table wants to get a deal. By working intensively and closely, we can achieve that deal."
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According to Mr Tajani, Mrs May also showed a willingness to consider the possibility of extending the proposed 21-month transition period following Brexit to three years.
He said: "Both sides mentioned the idea of an extension of the transition period as one possibility which is on the table and would have to be looked into."
