In May, Norbert Hofer of the anti-migrant Freedom Party (FPO) came within 31,000 votes of a far-right victory that would have resonated widely on a continent where mass migration driven by war and poverty threatens to polarise political debate.
The FPO then successfully challenged the narrow victory of Alexander Van der Bellen, an independent and former Green Party leader, citing procedural irregularities, forcing the re-run.
Recent opinion polls put Hofer ahead of Van der Bellen.
Sobotka said the re-run might now take place on either Nov. 27 or Dec 4, adding he was open to extending the vote to citizens who had reached the voting age of 16 since the spring.
That would require parliamentary approval, while postponing the re-run will require a change to Austria's electoral law.