Nicos Anastasiades said all EU leaders consider it a "bad precedent" for Cyprus or any other country to breach bloc rules and grant such key freedoms to third-country citizens.
Greek and Greek Cypriot officials accuse Turkey of obstructing the peace talks for the divided island because its demand to keep troops and military intervention rights after reunification.
A United Nations envoy has urged the rival sides on the divided island of Cyprus to seize an opportunity for peace, warning it could be years before such a chance arose again.
The division of Cyprus is now in its 43rd year. Next week may mark the decisive moment when the small eastern Mediterranean island nation starts to be stitched back together again.
Juncker faces renewed claims that he impeded EU moves against corporate tax avoidance when Luxembourg's prime minister, casting a shadow over his political future as a tussle over the bloc's top jobs looms.