Avramopoulos spoke in Nicosia after talks with his Greek Cypriot counterpart, Erato Kozakou-Marcoullis, on Sunday, the day Greek Cyprus assumed the EU's six-month rotating presidency.
Cyprus is divided into an internationally recognized Greek Cypriot south and a Turkish Cypriot north. UN-backed talks between the two sides to reunite the island under a federal government have so far failed to yield a breakthrough.
Ankara, which does not recognize the Greek Cypriot government, has said it will suspend dialogue with the EU presidency during the Greek Cypriot term. Turkey has also protested Greek Cypriot oil exploration in the eastern Mediterranean, saying the Turkish Cypriots also have rights to the natural resources of the island.
Avramopoulos said Turkey should realize that Greek Cyprus' EU membership and the discovery of natural gas off its southern coast could be opportunities to help the reunification effort.