"We consider that it is important for these conditions to be fulfilled, otherwise this deal between the EU and Turkey will not happen," Juncker told a forum organized by German broadcaster WDR.
"If Mr Erdogan wants to pursue his strategy, then he has to answer to the Turkish people why Europe is denying free travel to Turks. That's not my problem. That will be his problem."
The EU had dangled the promise of visa-free travel to Turks as part of a landmark March deal between Ankara and Brussels under which Turkey would help reduce the flow of migrants.
But the EU has set 72 criteria for Turkey to meet in order to win visa liberalization, among them is a condition for Ankara to change its anti-terror law.
Germany Thursday also stepped up its calls for the anti-terror law to be amended, with Foreign Minister Frank-Walter Steinmeier saying that in deciding whether to grant visa liberalization, the EU is waiting to see "the readiness of Turkey to end persecution of journalists through the usage of an anti-terror law".
"I don't have an influence on that, the ball is on the Turkish side," he said at the WDR forum, AFP reported.
Separately, German Deputy Chancellor Sigmar Gabriel, speaking at a separate press conference, urged Ankara to "allow the opposition and journalists to do their jobs" rather than use the law to "brand them as terrorists and locked away".
But Erdogan Thursday rebuffed the calls firmly, declaring that Turkey would not bow to the demand of amending its anti-terror law.
Instead, he accused the EU of "hypocrisy".