The Greek army on Thursday staged a double military exercise on its border with Macedonia and an island cluster near Turkey, officials said, amid tension with Skopje over the refugee crisis.

"Emergency manoeuvres have been ordered in Kilkis (in northern Greece) and Oinousses (in the eastern Aegean)," an army general staff source told AFP.

Another general staff source added that the exercise in northern Greece involved an airborne special forces unit backed by air support.

The second exercise in the Oinousses area, centred on the island of Chios, would involve anti-aircraft units, the second officer added.

Near Kilkis, an AFP reporter said warplanes were seen flying above the border camp of Idomeni which is housing some 11,000 refugees and migrants -- many of them Syrian families suffering from the experience of air raids during the civil war in their country.

An airforce source said the areas chosen for the exercise were "in the news" in recent days.

Greece this week said Turkish warplanes had repeatedly entered the Athens flight information region (FIR), flying over the Oinousses island cluster.

Turkey disputes whether the area should be administered by Greece.

On Sunday, Greek media said Macedonian riot police had briefly entered Greek territory to push back migrants attempting to breach a wire fence on the border with Greece.

The Greek government later strongly denied this.

"We have to instill a sense of security to people (living on the border)," a military source told AFP.

The Macedonian operation on Sunday sparked a political row, with Greek Prime Minister Alexis Tsipras accusing Skopje of "shaming" Europe by using tear gas and rubber bullets against unarmed migrants.

Macedonia denied using rubber bullets and said the migrants had thrown stones at its officers, injuring several.