France's foreign ministry has urged Turkey to end its assault on Kurdish fighters in northern Syria.
Turkish troops shell Kurdish positions in Syria. Photo: AFP
In a statement (in French) it said it was "worried about the continued worsening of the situation".
On Saturday, Turkey began shelling the militia, which it said was linked to the banned Kurdistan Workers Party (PKK).
The fighters, the YPG militia based in Syria, have rejected Turkey's demand to leave areas it has seized, saying Islamists would return if it left.
Turkey's assault is a new thread in an already-complex conflict that has drawn in competing regional powers.
Turkish Prime Minister Ahmet Davutoglu insisted on Sunday that Turkey "will not permit the [Kurdish militia] to carry out aggressive acts".
"Our security forces gave the necessary response and will continue to do so," Mr Davutoglu said.
A statement on Syria's state news agency also condemned Turkey's intervention, calling it "outrageous violation of international law".
France also called on the Syrian regime and its allies to stop their bombardments "across the whole of the country".
France said priority should be given to implementing an agreement reached in Munich this week on ceasing hostilities, and the fight against so-called Islamic State (IS) group.
Almost five years of civil war in Syria have led to the deaths of more than 250,000 people. About 13.5 million people have been displaced.
Attempts to broker a peace deal have repeatedly failed, but on Thursday, world leaders agreed to work towards a so-called cessation of hostilities in Syria within a week.
The US and Russian presidents agreed in a "frank and business-like" phone call to work more closely to achieve this, the Kremlin said on Sunday.
Russia, an ally of Syrian President Bashar al-Assad, has been carrying out air strikes since September against what it terms "terrorists".
Among the targets shelled by Turkey was the Menagh airbase, which was seized by the YPG on Thursday from Syrian Islamist rebels. The YPG controls much of Syria's northern border with Turkey.
Turkey's state-run Anadolu Agency said Turkish forces shot at Kurdish fighters inside Syria on Sunday after coming under fire themselves.
Ankara sees the group as being linked with Kurdish guerrillas from PKK, which has waged a campaign against security forces in Turkey for decades.
Under the agreed cessation of hostilities plan, efforts will be made to try to make urgent aid deliveries to besieged and hard-to-reach areas in Syria.
Steps will also be taken to work towards an eventual ceasefire and implementation of a UN-backed plan for political transition in Syria.
The halt would not apply to the battle against the jihadists of IS and al-Nusra Front.
However, neither the Syrian government nor the rebels were involved in the deal and both have since vowed to continue fighting.
Syrian President Bashar al-Assad said on Friday that he intended to retake "the whole country" from rebels - a statement the US government said was "deluded".
Syrian government forces, backed by Russian air strikes, have almost encircled rebels in parts of the northern city of Aleppo.
Also on Sunday, Russian Prime Minister Dmitry Medvedev repeated a warning that any foreign ground operation in Syria would lead to "a full-fledged, long war".
Turkey has said its troops and forces from Saudi Arabia might participate in a ground operation against IS.
- BBC