The French sailors were trying to check a cargo ship a few weeks ago on suspicion it was taking arms to Libya -- forbidden under a UN embargo

Turkish frigates carried out radar targeting three times, suggesting a missile strike was imminent, the ministry said.

"This is an extremely aggressive act that is unacceptable by an ally against a NATO ship," said a ministry official who did not want to be identified by name.

"We consider this an extremely grave matter" and "we cannot accept that an ally behaves this way, that it does this against a NATO ship, under NATO command, carrying out a NATO mission," the official said.

The disclosure of the incident comes with NATO defence ministers scheduled to hold talks via videoconference on Wednesday.

Tensions between France and Turkey, which is also a NATO member, have flared recently over their roles in the civil war in Libya.

Turkey supports the UN-recognised government in Tripoli, while France is suspected of favouring the military strongman Khalifa Haftar, based in eastern Libya.

This week, Ankara condemned "unacceptable" criticism from France over its shipments of weapons and fighters to the Government of National Accord (GNA), which Paris calls a "direct violation" of the United Nations embargo.

"These waves of boats between Turkey and Misrata, sometimes escorted by Turkish frigates, are not contributing to any de-escalation," the French ministry official said Wednesday.