Stocker said he had been authorised by his party to enter into coalition talks with the far right if invited to do so.
“This country needs a stable government right now, and we can’t keep losing time to election campaigns or elections that we don’t have,” Stocker said.
Shortly before, Austria’s President Alexander Van der Bellen announced he would meet FPOe leader Herbert Kickl at 1000 GMT on Monday to “discuss the new situation”.
“Voices within the OeVP that rule out working with…. Kickl have become significantly quieter,” Van der Bellen told reporters.
“That means a new path may be opening up that did not previously exist,” he said, adding that he will appoint a caretaker chancellor in the coming week.
In a press conference, Stocker welcomed the president’s decision to hold talks with the far-right leader, whose party won almost 29 percent of the vote, but has so far been unable to find partners to form a national government.
Far-right government ‘highly likely’
It was not immediately clear whether Van der Bellen would task the far-right leader with trying to form Austria’s next government.
Van der Bellen had initially tasked the conservatives with forming a stable government that respects the “foundations of our liberal democracy”.
In the past, he had voiced reservations about Kickl, whose party currently polls at around 35 percent.
Policial scientist Thomas Hofer told AFP that a coalition led by the far right with the conservatives as junior partners had become “highly likely”. The OeVP “can’t afford” snap elections, he argued.