Kurz -- whose country holds the bloc's rotating presidency -- said after meeting Dutch Prime Minister Mark Rutte that the European Union would do "everything possible" to avoid a no deal scenario.
"In the end we will find a way to deal with the UK," the youthful Austrian leader told a press conference with Rutte in The Hague.
"We will do everything possible to avoid a hard Brexit. And I think there is no alternative to find a solution together, it is in the interest of the UK, but it is also in the interest of the EU 27."
Kurz joined a chorus of both British and European leaders insisting a deal was still possible despite fresh Brexit talks in Brussels breaking down on Sunday.
The leaders were speaking two days before heading to Brussels for a summit of EU leaders that had been billed as a "moment of truth" ahead of Britain's exit from the bloc in March.
Rutte said a deal was "very close" but called for "maximum creativity" over the major sticking point in the Brexit talks -- how to keep open Britain's land border between Northern Ireland and EU member Ireland.
"We are cautiously optimistic but still a lot needs to be done, particularly on the issue of the border," Rutte said.
"We both hope that over the next 24 hours and maybe during the summit itself we will come to a conclusion on the right way," he added.
"We need a little bit more time. But as Theresa May said today in parliament, we are very close."
May will update the other 27 EU leaders before their dinner in Brussels on Wednesday, with the summit kicking off on Thursday, her Downing Street office confirmed.