Austrian Chancellor Christian Kern said the negotiations were "no more than fiction" and "Europe needs a new path".
Turkey's EU Affairs Minister Omer Celik said his comments were "disturbing" and "similar to far-right rhetoric".
Turkey's crackdown since a failed coup on 15 July has fuelled alarm in the EU. Mr Kern said democratic standards in Turkey were far from EU requirements.
Austrian Defence Minister Hans Peter Doskozil has criticised "signs of a dictatorship" in Turkey, and called for an end to its EU accession talks.
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European Commission President Jean-Claude Juncker agreed that "Turkey cannot become a European Union member in its current state".
But he rejected the Austrian position. "I don't think it would be helpful if we were to tell Turkey unilaterally that the negotiations are over," he told German ARD news.
In 2005 Turkey began negotiations to join the EU, but progress has been extremely slow. Many European politicians are against Turkey joining, although it is an official candidate.
Turkey has urged the EU to grant visa-free travel to Turks wishing to visit the Schengen zone, covering most of Europe.
The EU offered visa liberalisation as part of its March deal with Turkey, aimed at curbing the flow of migrants from Turkey to Greece.
But the EU attached stringent conditions to the travel offer - and so far, the EU says, Turkey has only fulfilled some of them.
Turkey country profile
More than 50,000 Turks have been detained or sacked over suspected links with the alleged mastermind of the coup plot, Fethullah Gulen. The US-based cleric denies any role in the attempted overthrow of President Recep Tayyip Erdogan.
Turkey has been accused of abusing anti-terrorism laws to silence critics of Mr Erdogan.
According to Mr Celik, Turkey still holds EU "core values" as its benchmark.
He said "criticism is a democratic right but there must be a distance between criticising Turkey and an anti-Turkey attitude".
Turkey has angrily rejected Austrian suggestions that its membership talks with the EU should be ended.