Ships from Italy, Slovenia, Montenegro and Albania will take part in the exercise as well.
The purpose of the exercise is to strengthen cooperation and inter-operability between the participating countries' navies.
The ships will rehearse the planning and implementation of naval operations to enable joint action and fast exchange of information in search and rescue operations at sea, as well as procedures taken when a ship is suspected of carrying illegal cargo.
After Greece, the "Fraust Vrancic" will pay a friendly visit to the Turkish port of Izmir, where it will stay until July 6.