Fears are growing that Britain will leave on March 29th, 2019, without a withdrawal agreement, mainly due to the difficult issue of how to avoid border checks between EU member Ireland and the British province of Northern Ireland.
"I very much hope that we can also resolve the difficult issue with Northern Ireland and the potential border. If it is not possible to find a solution, then I plead for the negotiations to be continued, but that we do not allow a hard border in any case," Kurz, whose country has just taken on EU presidency, told a press conference in Vienna.
"Our goal is that we reach an agreement with the UK. But if that's not possible, we have to avoid a hard Brexit. So our goal is clear, but if not, I think it's good to keep negotiating," Kurz said.
Asked if that meant extending the EU's so-called Article 50 process – which allows for just two years between a country's notification of withdrawal and the day it leaves – Kurz said "we will see".
Kurz said he would visit Britain and Ireland next week for talks with Prime Ministers Theresa May and Leo Varadkar.
The intervention by the youthful leader who will lead the EU presidency for the next six months comes as May prepares to present her new plan for post-Brexit EU relations to solve the Irish border plan.
But her ideas are likely to be rejected not only by hardline members of her own cabinet, including Brexit minister David Davis, but by Brussels itself.
The EU has faced growing calls to compromise over its red lines for Brexit, which include avoiding a "hard" Irish border, and a refusal to let Britain "cherry-pick" the benefits of the single market while dismissing its obligations including unlimited immigration.
On Ireland, the EU has insisted on a "backstop", which would see Northern Ireland remaining under EU customs laws for an undetermined time after Brexit. Britain says this is an unacceptable attack on its sovereignty.
Kurz, however, insisted that the remaining 27 EU states had to stick together.
"The most important thing is that we preserve the unity of the 27 and also that we will not let ourselves be divided," he said.