Turkey shelled Kurdish positions in northern Syria repeatedly over the weekend, defying French and American calls to end the attacks.
The Kurdish YPG militia took a former Syrian military air base near the Turkish border last week as it advanced east across formerly rebel-held territory, prompting furious calls for withdrawal from Ankara.
On Saturday, the Turkish prime minister, Ahmet Davutoglu, confirmed the cross-border shelling, insisting that his military would retaliate against “every step” made by Kurdish forces.
Turkish media said the army was using howitzers on Kurdish targets near the Syrian town of Azaz.
The YPG, which is the main Kurdish militia in Syria, is taking advantage of a Syrian offensive against rebel forces in northern Aleppo, moving in on Azaz and the town of Tal Rifaat in an attempt to expand its hold on land along the border.
Turkey sees the YPG as an extension of the PKK, a Kurdish group that has been waging a bloody insurgency on Turkish soil over much of the past three decades.
Its disquiet has also been heightened by the arrival of tens of thousands of fleeing civilians on its border in recent weeks.
At least 35,000 Syrians are camping out on the southern border while new arrivals in Azaz could yet be pushed northwards to join them.
With more than 2.5 million refugees already living inside Turkey’s borders, Ankara is desperate for Western countries to shoulder more of the burden from Syria’s humanitarian crisis.
Echoing an appeal made by the United States on Saturday, France called last night for “an immediate halt to the bombing, both that of the regime and its allies throughout the country and that of Turkey in the Kurdish zones”.
Washington has been working closely with Kurdish forces in northern Syria against Isil – so Nato finds itself on both sides in the war.
The YPG in Aleppo has also been supported by Russian bombing raids, with Moscow claiming that the rebels they are fighting are dominated by the al-Qa’ida affiliate Jabhat al-Nusra.
Russian President Vladimir Putin and President Barack Obama spoke by telephone, calling for the implementation of a ceasefire that they agreed last week.
But Sergei Lavrov, the Russian foreign minister, said that he thought the chances of its coming into effect were less than 50pc.
The state-run Anadolu news agency said that the attacks were launched in retaliation for incoming fire from the People’s Protection Units.
Analysts said Turkey was alarmed that the YPG has taken advantage of losses suffered by Arab rebel groups to gain new territory.
The five-year conflict in Syria has not only spilled over into neighbouring countries – but has also become an arena for international rivalries, pitting Syrian President Bashar al-Assad’s allies Russia and Iran against his opponents the United States, Europe, Saudi Arabia and Turkey.
Major powers reached a surprise agreement in Munich last week on a “cessation of hostilities” in Syria, which is due to come into force by the end of this week.
However, even the deal’s own architects have voiced scepticism about the prospects of success.
Russia, in particular, stands accused of duplicity over its campaign of air strikes.
Moscow argues that it only targets Isil and other “terrorists”, but Washington says Russia is mainly hitting rebel forces who are fighting the Syrian army.
President Obama spoke to President Putin yesterday and urged him to stop bombing “moderate” Syrian rebels, while the British Foreign Secretary Philip Hammond accused Moscow of “carpet-bombing” civilians.
The Kremlin said Russia was “positive” about the Munich deal but promised to continue bombing “terroristic organisations”, a term it uses to describe all those battling to topple the Syrian government.
Iran said yesterday that it would be willing to provide air defence systems to the Syrian government.
The offer came after Tehran’s arch-rival Saudi Arabia said that it could send ground troops and warplanes to fight Isil in Syria and warned that President Assad may have to be removed “by force”.