Earlier this week Cyprus said it had issued arrest warrants for the crew of a Turkish drilling ship which it said had infringed on its territory.
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At a summit in Malta, the EU's Mediterranean states have backed up fellow member state Cyprus in its dispute with Turkey over lucrative offshore gas reserves.
The discovery of the reserves has worsened long-running tensions between Turkey and Cyprus.
Earlier this week Cyprus said it had issued arrest warrants for the crew of a Turkish drilling ship which it said had infringed on its territory.
Ankara said reports of the arrest warrants "crossed the line" and insists it has the legal right to conduct energy research in waters off Cyprus.
On Friday, French president Emmanuel Macron said the EU "will not show weakness on this matter."
"I want to reiterate my solidarity with Cyprus and my support and respect for its sovereignty. Turkey must stop its illegal activities in Cyprus's exclusive economic zone."
Turkey invaded the northern third of the island of Cyprus in 1974.
The Turkish-speaking northern part of Cyprus proclaimed independence but is recognised only by Turkey.
Decades later the island still hosts a UN peacekeeping force which separates Greek Cypriots in the south from Turkish Cypriots in the north.
Turkey has bid for EU membership, but its candidacy is frozen, with the EU executive in May saying its hopes of joining were fading because of backsliding on rights and rule of law.