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.
An additional Brexit summit could be held in November, but only if a deal is within reach.
May has told lawmakers that they will vote either for a Chequers-based deal or to leave without an agreement.
But just minutes after he spoke, May insisted that her Brexit plan was the "only serious and credible" proposal on the table.
Specifically, he said that he would "clarify" which goods will have to be checked by customs officers as they are transported between mainland Britain and Northern Ireland.
Donald Tusk, EU Council president, said key parts of the British proposals "will not work".
Speaking after her meeting with Mr Tusk, she said: "We both agree there can be no withdrawal agreement without a legally-operative backstop".
I think most of us would welcome a situation where there is the possibility of the British people putting things into perspective, seeing what has been negotiated, seeing the options and then deciding once and for all.
But "unfortunately we can not at this stage exclude a no-deal - it depends on both sides of negotiations". So don't worry, be happy, don't worry.
And Tusk suggested to the media that she had failed to convince a single European Union leader.
The European Union's chief Brexit negotiator Michel Barnier said on Tuesday the bloc was ready to improve its proposal for an "insurance policy" backstop arrangement on how to manage its Irish border that would avoid creating a physical customs border on the Irish Sea.
May was also set an October deadline for a solution on the Irish border issue just hours after informing Leo Varadkar, the Irish taoiseach, in a private breakfast meeting that she felt it would be impossible to come to a compromise within such a timescale. Various scenarios are still possible today, but I would like to stress that some of Prime Minister May's proposals from Chequers indicate a positive evolution in the UK's approach as well as a will to minimise the negative effects of Brexit. However, leaders are now preparing for an extended timeline.
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.
However, at the gathering in Austria, Mrs May insisted there would be no delay to the UK's March 2019 departure, no second referendum and therefore the onus was on the continent's leaders to find a solution if they wanted to avoid a no-deal Brexit.
The UK industry - already feeling the effects of a crackdown on diesel-powered cars in its largest European Union markets amid jittery demand - fears Brexit could result in lost access to vital European Union workers and massive costs from tariffs and additional red tape including supply chain disruption.
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