Turkey will not allow the Syrian border town of Azaz to fall to Syrian Kurdish fighters, Prime Minister Ahmet Davutoglu said on Monday, warning of a "severe response" if they advance.

"We will not let Azaz fall," Davutoglu was quoted as saying by private NTV television on his plane en route to Ukraine.

"The YPG (the People's Protection Units, a Syrian Kurdish militia) will not be able to cross to the west of the Euphrates (river) and east of Afrin," he added.

Turkish artillery has struck at Kurdish militia targets in Syria since the weekend, with Ankara insisting it was returning fire.

Ankara accuses the YPG of being the Syrian branch of the Kurdistan Workers' Party (PKK) which has waged a decades-long insurgency against the Turkish state, and it fears Syrian Kurds are seeking to carve out an autonomous Kurdish region on Turkey's border.

Turkey confirmed on Monday that it shelled advancing Kurdish fighters in northern Syria for a third day.

Foreign ministry spokesman Tanju Bilgic said Ankara "retaliated in kind" when an attack from an area under YPG control targeted a border post in Turkey.

The Damascus regime has condemned Ankara over the shelling while urging the United Nations to act.

"Currently YPG elements were forced out of the Azaz neighbourhood. If they come closer to Azaz, they will receive the most severe response," Davutoglu said.

"The necessary intervention will be made (by Turkey) against the YPG when it is required."

Turkey has been gravely concerned by the moves of the Kurdish fighters on Azaz and has so far defied calls from its Western partners to stop artillery bombardments of YPG positions

The Syrian Democratic Forces (SDF), a US-backed Kurdish-Arab militia alliance in which the YPG plays a key role, has also seized the Minnigh air base in northern Syria.

Davutoglu warned the SDF to withdraw from the airport, issuing a veiled threat of possible Turkish military action if they failed to do so.

"They will withdraw from the airport... "If not, the airport will be rendered unusable," he said, without elaborating.

Davutoglu said the "the YPG is clearly Russia's instrument in Syria right now," the state-run Anatolia news agency reported.

"Russia is using those tools to be able to corner Turkey. Therefore, our stance has a legitimate basis."

Russia is the key ally of the regime of Syrian President Bashar al-Assad, who Turkey wants to see ousted.

Relations between Ankara and Moscow nosedived after Turkey shot down a Russian war plane on the Syrian border on November 24. And Ankara accuses Moscow of bombing Syrian opposition forces backed by its Western allies instead of the Islamic State.

Turkey's opposition to the YPG and its political arm the Democratic Union Party (PYD) is also straining relations with the United States which supports the Syrian Kurds as effective fighters on the ground against Islamic State (IS) jihadists.

Washington has urged its key NATO ally to cease firing of Syrian Kurdish positions.

The Turkish government has also denied claims it sent troops into northern Syria, with Defence Minister Ismet Yilmaz saying late Sunday that Ankara has no intention of intervening on the ground.