The Turkish military confirmed Monday its forces shelled Syrian Kurdish positions of the PYG for a third consecutive day.
During a visit to Ukraine, Prime Minister Ahmet Davutoglu warned the PYG that it will face what he called the "fiercest response" if it makes further territorial gains.
Ankara accuses the group of being a terrorist organization linked to the Kurdish rebel PKK, which Turkish forces are fighting in Turkey.
The PYG is fighting to connect the last link in a continuous Kurdish-controlled region in Syria along the Turkish border.
With the Syrian Kurdish leadership dismissing Ankara's warning, Turkey's political leaders have not ruled out a military intervention. But retired Turkish general Haldun Solmazturk warned that any intervention would be extremely risky.
"The major military risk is a conflict with the Russian armed forces; it is inevitable. And besides, the Syrian regime forces would also resist and also various groups from Kurds to ISIL,” Solmazturk said, using an acronym for Islamic State. “I mean there are so many risks involved, currently Syria is a most complicated military environment for an army to intervene."
Since Turkish jets downed a Russian warplane in November, Moscow has installed a sophisticated anti-aircraft system to support its fighter jets and bombers operating in Syria.
What is more, international relations expert Soli Ozel warned that Russian President Vladimir Putin may be only too happy to see a Turkish intervention.
"I think the Russians are waiting eagerly for Turkey to take such a step, in order to get even for their downed plane,” Ozel said. “Putin, I think, wants to exact a punishment from Turkey."
Turkish news reports quote military leaders as saying that, under Turkish law, any intervention in Syria requires sanctioning by the U.N. Security Council.
Observers say Turkey might try to circumvent that law by declaring that its target is the Islamic State extremist group. But Ozel said domestic security concerns could ultimately prevent Turkey from sending an unwilling military into Syria.
"If the government insists that they must do it, it will be done,” Ozel said. “But can a government really push a military that obviously for good reasons is reluctant to do such a thing? Especially if that military is now fighting domestically in Turkey an extraordinary brutal and fierce battle against the PKK, which is also a big priority for the government?"
Major security operations are continuing across towns and cities in Turkey's predominantly Kurdish southeast against the PKK. During spring, with winter snows melting, the PKK are expected to emerge from their winter hideouts and escalate their operations across the region.