Turkey's longstanding, and recently revived, bid to join the EU has already been hit by President Recep Tayyip Erdogan's suggestion that he may reintroduce the death penalty after the July 15 attempted putsch.
But after Austria raised the prospect of slamming the brakes on membership talks, Juncker called for calm.
"If one gives the impression to Turkey now that, no matter what, the EU is not ready to take in Turkey, then I would say that is a serious foreign policy mistake," Juncker told German public broadcaster ARD.
"I don't see this willingness among all member states at this point in time" to break off talks, he said.
Also Read
At the same time, Juncker acknowledged that Turkey has work to do in order to meet membership conditions set by the bloc.
"Turkey cannot be a member of the European Union in its current state, and especially not if it decided, as some have warned, to reinstate the death penalty. That would lead to the immediate breaking off of negotiations," he warned.
Ankara had signalled that it could ditch a controversial deal with the EU to halt migrant flows to Europe, if the bloc failed to meet its promises including granting visa-free travel to Turks as well as accelerating membership talks.
Juncker himself had warned last week that the pact was at risk of breaking down.
Austria ratcheted up tensions today when Chancellor Christian Kern called for the EU to discuss ending accession talks with Turkey.
"We know that Turkey's democratic standards are far from sufficient to justify its accession."
Asked by public broadcaster ORF whether he wanted to halt the talks, Kern said he would initiate a debate on the matter at a summit of leaders on September 16.