Downing Street said Chancellor Sebastian Kurz agreed that Britain’s departure from the EU would be on the agenda for the European Council being hosted by his country – which currently holds the EU presidency – on September 20.
It means that the Prime Minister has an extra gathering of leaders of the EU 27 in which to convince them to support her Brexit plan after a week in which ministers have been deployed to various capitals to woo senior politicians.
The next meeting is a gathering of EU leaders in Brussels in October by which time it has been hoped a Brexit deal will be hammered out.
May was dealt a blow by Brussels on Thursday as its chief Brexit negotiator, Michel Barnier, rejected the customs proposals that form a key plank of her White Paper.
A Downing Street spokesman said: “Following their dinner at Downing Street three weeks earlier, the Prime Minister and Austrian Chancellor Sebastian Kurz had a positive conversation ahead of the Salzburg Festival.
“The Prime Minister updated on the White Paper, and Chancellor Kurz confirmed that Brexit would be on the agenda for the informal European Council which Austria would host on 20 September.”
May also pitched her deal planning to her Czech and Estonian counterparts, Andrej Babis and Juri Ratas, during talks at the Salzburg Festival.
May attended the music event before heading off to Italy for the start of her summer holidays.
Ahead of their meeting, Mr Kurz said it was important to “avoid a hard Brexit”.
It came as the head of a pan-European dairy co-operative warned that a no-deal Brexit would risk soaring prices and supply problems getting products to consumers.
Ash Amirahmardi, UK managing director of Arla Foods, spoke after ministers last week raised the spectre of foods and medicines being stockpiled as part of contingency planning in case the UK leaves the EU without a deal in place on customs.
Amirahmardi told BBC Radio 4’s Today programme that 16% of UK dairy products are imported, and of those 98% were from Europe, saying: “If we have barriers at our ports then that is what is going to lead to increased prices and potentially supply issues.”
He added that World Trade Organisation (WTO) tariffs – which would come into play if there was no Brexit deal – on dairy products are “penal” and that stockpiling produce is “not something that is really practical for the dairy industry”.
He said the average person in the UK consumes the equivalent of three pints of milk per day, adding: “One of the reasons they do is because of the nutritious benefits of it, but it is also accessible in terms of prices.
“Any increase in the friction of movement of products will inevitably lead to higher costs and therefore one of our concerns is to make sure consumer prices are accessible post-Brexit.”
It comes after a successful week for those hoping to stop Brexit, as public support begins to tip in favour of a second vote on the final exit deal.