"Turkey's declared intention to illegally conduct a new drilling operation northeast of Cyprus is of grave concern," EU top diplomat Federica Mogherini said in statement.

Turkey's first drilling attempts prompted EU leaders in June to warn Ankara of "targeted and appropriate" sanctions if it did not stop its "illegal activities".

According to the EU statement on Monday, the European Council is considering "appropriate measures" and will respond "in full solidarity with Cyprus" in light of this second exploration.

Mogherini reiterated the call to Turkish authorities "to refrain from such actions, act in a spirit of good neighbourliness and respect the sovereignty and sovereign rights of the Republic of Cyprus in accordance with international law".

Ankara has sent a second ship -- the Yavuz -- for exploratory activities off eastern Cyprus, after its Fatih vessel entered the island's exclusive economic zone in the west in May.

"This second planned drilling operation... is a further unacceptable escalation which violates the sovereignty of Cyprus," Mogherini added.

The region near the island is believed have rich natural gas deposits, triggering a race between Turkey and Cyprus, which has ramped up exploration in the eastern Mediterranean.

Hours earlier, Cyprus condemned Turkey's actions "in the strongest of terms", in a statement from the Cypriot presidency.

It said the second attempt was taking place off the Karpas peninsula, in the northeast of the island, and amounted to "an escalation of continued violations by Turkey".

The Cyprus government said "Turkey continues to violate international law... disrespecting the calls of the European Union and the international community".

Ankara says its actions abide by international law and that it is drilling inside its continental shelf.

Cyprus has said only a resumption of talks aimed at reaching a peace settlement between the Turkish-held north and the internationally-recognised government in Nicosia could resolve the dispute.

The island has been divided between the Republic of Cyprus and the northern third under Turkish military control since 1974, formed after a Turkish invasion in response to a coup sponsored by a Greek military junta.

Cyprus has issued arrest warrants for Fatih's crew members, accusing the ship of breaching the republic's sovereign territory.

Turkey opposes unilateral exploration activities by Cyprus and says Turkish Cypriots have rights to a share of the island's offshore resources.