NATO started patrolling the Aegean Sea between Greece and Turkey at the end of February in an effort to "cut the lines of illegal trafficking and illegal migration," a statement from the organization says.
There are four frigates included in the mission, one each from Germany, Canada, Turkey and Greece. It is currently German-led.
The vessels are conducting "reconnaissance, monitoring and surveillance activities," the statement says, while the crews are performing drills.
Crew members are practising how to retrieve migrants from the sea if they come into distress, in accordance with international conventions.
The operation is not focused on rescue activities, but any migrants in distress rescued by NATO vessels will be taken back to Turkey if they set off from there, the alliance has said.
"We are currently operating in an area where the probability of running across a refugee or migrant boat is a lot higher than in other areas," Rear Admiral Joerg Klein said in a statement.
"Therefore I want the units of our multinational force to be able to handle such a situation quickly and professionally."
The frigates have speedboats to enable them to approach crafts containing migrants and, if necessary, to rescue anyone in the water.
The mission also has the use of helicopters for reconnaissance and monitoring activities.
The NATO vessels aim to work in cooperation with Greek and Turkish authorities, as well as with the European Union's external border agency, Frontex.