Tusk agreed May's Chequers proposals "will not work, not least because it risks undermining the single market" of seamless movement of goods, services, capital and persons.
"If the political will is there on the other side I am confident we will reach a deal which is in the EU's interests as well as the UK's", she said.
The next major milestone in the Brexit process is fast approaching, with the October 18 summit labelled a "moment of truth" by Tusk.
Under Chequers, Britain would basically remain a member of the EU's single market for goods and abide by European Union rules governing that market. But she showed no sign of backing down from the proposals hashed out with her Cabinet at her country retreat of Chequers in July - so controversial with her own party that they provoked the resignation of her foreign secretary, Boris Johnson, and Brexit secretary, David Davis.
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.
Mrs May faces a fight with angry Conservatives at her party's conference in 10 days.
If 40 of May's 315 lawmakers and the opposition parties voted against a Brexit deal based on her proposals, she would fall short of the number needed to pass the legislation.
In a letter to opposition leaders at Westminster, Nicola Sturgeon yesterday called for the Brexit timetable to be extended in the event that no deal is reached, to "avoid an economic cliff edge".
Mrs May remains wedded to the Chequers blueprint, noting it is the only proposal on the table as the deadline approaches, although she indicated the United Kingdom will unveil new measures on the future status of the Northern Irish border in a bid to break the deadlock.
"We're ready for that eventuality, should it occur".
Eventually one side - or more likely, both - "is going to have to blink to avoid no deal, and Downing Street is hoping that the PM has done enough to get Brussels to budge more", says The Times's Matt Chorley.
"It was clear today that we need substantial progress by October and that we then aim to finalise everything in November", Dr Merkel told reporters as the summit ended.
With barely six months until Britain leaves the European Union, there is pressure on both sides as any failure to strike a deal to tie up legal loose ends brings the risk of serious disruption.
May says she can not accept having customs checks within the United Kingdom.
Taoiseach Leo Varadkar - who met Mrs May on the sidelines of the summit - said there are elements of the Chequers plan that can inform further negotiations and indicated there is room for compromise once the fundamental demands of Ireland and the European Union are met.
But with the talks deadlocked, Kurz confirmed Thursday there would be a final summit in November to clinch the deal.
Irish deputy prime minister Simon Coveney, asked if this was an attempt to humiliate Mrs May in Salzburg, told Newsnight: "I certainly hope not".