She will then be out of the room when the other 27 leaders discuss her Brexit proposals over lunch, and will find out about their reactions only when summit chair Donald Tusk briefs her separately afterwards.
May defended her Chequers proposal for Brexit on Wednesday when arriving in Salzburg by saying that "It's the only credible and negotiable plan on the table that delivers no hard border in Northern Ireland and also delivers on the vote of the British people".
United Kingdom officials played down the EU's tough talk on Chequers as a long-expected negotiating tactic that would not throw the prime minister off course.
Despite reports of a friendly spirit at a summit in Salzburg, Austria, the fundamental differences remained.
Speaking after her meeting with Mr Tusk, the PM said: "We both agree there can be no withdrawal agreement without a legally operative backstop". He wants to see a major breakthrough by the time the leaders meet again in Brussels on October 18-19. Tusk, meanwhile, said that the upcoming October summit would be the "moment of truth" for reaching a deal, and that "if the conditions are there" another summit would be held in November to "formalize" it.
"Those to the right of the party - the pro-Brexit wing will be very concerned that if that deal doesn't prevail, they'll end up in the situation where we could have a second referendum and we could end up not leaving the European Union altogether", he said.
Malta's prime minister on Thursday (20 September) signalled unexpected support from European Union leaders for a second referendum on Brexit in Britain, boosting a growing campaign for a new poll despite the British government's trenchant opposition.
"Neither side can demand the unacceptable of the other, such as an external customs border between different parts of the United Kingdom", May wrote in Die Weit. We are hiring extra staff and officials, bringing in IT systems.
"We're ready for that eventuality, should it occur".
And Tusk suggested to the media that she had failed to convince a single European Union leader.
President Emmanuel Macron of France was scathing.
"We all agreed on this today, the proposals in their current state are not acceptable, especially on the economic side of it".
"Not least because it risks underlining the single market..."
Paul Whiteley, a professor of politics and government at the University of Essex, explains the latest on the unfolding Brexit process.
Following two days in Salzburg, the British prime minister appeared to stick to her guns on the blueprint which is centred on a "common rulebook" approach, arguing that it was the only proposal that would avoid a hard Border in Ireland. Failing to do so could disrupt the lives of people and business on both sides, and undermine Northern Ireland's hard-won peace.
BMW ( BMWYY ) said Tuesday that it would shut its Mini factory in England for one month of maintenance immediately after Brexit because it can't be sure of getting the parts it needs.
Before setting off, her Downing Street office suggested that after she put forward new Brexit proposals this summer, it was now for Brussels to "evolve" its position.
Her Chequers plan also faces opposition from pro-Brexit members of her own Conservative Party, who say it would keep Britain tethered to the bloc, unable to strike new trade deals around the world.
The denial of Chequers from European Union leaders came after Sir Mike Penning, a ally of May, said MPs would vote down the Chequers proposal because it "doesn't deliver what people ask for".
An emergency summit on Brexit proposed for November 17-18 will only happen as a "punchline to effective negotiations", Tusk said.
- Dutch Prime Minister Mark Rutte said his country is better prepared for a no-deal Brexit than Britain and an agreement is "not easy" because of Mrs May's red lines.
Concern was mounting at the informal summit that no final Brexit deal will be approved ahead of the March 31, 2019 deadline and that no plan for a smooth and orderly British exit from the bloc.