Arriving for the two-day summit, May accepted that her 27 European Union counterparts were unlikely to agree that there has been enough progress on divorce issues to move on to a second phase, saying the meeting was intended to "take stock".
But she urged them to start preparations to discuss trade and a transition deal at the next summit in December, telling reporters they would be "setting out ambitious plans for the weeks ahead".
She said a deal to secure their rights was "within touching distance" - but also told reporters that she wanted EU leaders to show "an urgency in reaching an agreement".
EU President Donald Tusk warned he did "not expect any kind of breakthrough", saying that while there had been "promising progress", London needed to come up with more concrete proposals.
The talks had to be moved at the last minute from the EU's new 321-million-euro Europa summit building after noxious chemicals in the catering area sickened several people yesterday
"Lessons from #EUCO kitchen: fuming over #Brexit must not become toxic," Lithuanian Prime Minister Dalia Grybauskaite said on Twitter.
The EU agrees that of the three key separation issues at stake, citizens rights is the most advanced, but sticking points remain. Discussions on the bill Britain must pay to leave meanwhile are deadlocked and discussions on Northern Ireland still have far to go.
She will then leave them to discuss Brexit without her tomorrow morning.
After five rounds of Brexit negotiations produced few results, fears are growing that Britain may fail to strike a withdrawal agreement before its formal departure on March 29, 2019.
May engaged in a whirlwind of diplomacy ahead of the summit, calling the French and German leaders among others and having dinner with European Commission chief Jean-Claude Juncker in Brussels.
Britain's exit bill is the most poisonous issue. In a speech in Florence last month, May promised to maintain Britain's contributions for two years after Brexit to complete the current EU budget period, totalling around 20 billion euros (USD 24 billion).
Germany and France insist that there should be no impact on the EU's budget from Britain's departure.
But European Parliament chief Antonio Tajani - whose institution will have a final veto on any Brexit deal - told the BBC that "20 billion is peanuts. The problem is 50 or 60 (billion euros).
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