Ankara (AFP) - Turkey will continue to strike back at Kurdish fighters of the Democratic Union Party (PYD) in Syria, Prime Minister Ahmet Davutoglu told German Chancellor Angela Merkel on Sunday, despite growing pressure on Ankara to stop the shelling.

In telephone talks, Davutoglu told Merkel that Turkey "will not permit the PYD to carry out aggressive acts. Our security forces gave the necessary response and will continue to do so," his office said in a statement.

Turkish artillery struck at targets of the PYD and its People's Protection Units (YPG) militia on both days of the weekend, while insisting that it was returning fire under the rules of engagement.

Davutoglu alleged to Merkel that the Syrian Kurdish forces, who Turkey accuses of being the Syrian branch of the outlawed Kurdistan Workers' Party (PKK), had been advancing with Russian air support.

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

He said the move by the Kurdish fighters was aimed at uprooting "hundreds of thousands of Syrian civilians" from the border region and "creating a new humanitarian crisis" that would affect both Turkey and the European Union.

"This is aimed not just at Turkey but also the European Union," he said, warning of a "new wave of hundreds of thousands of refugees".

The EU and Turkey, which hosts over 2.5 million Syrian refugees, are already grappling with the crisis that saw around one million migrants cross the Aegean Sea from Turkey to the EU in 2015.

France had earlier called for an "immediate halt" to Turkey's artillery bombardments while the US State Department had also urged Turkey to cease firing.