Russian Defence Minister Sergei Shoigu said Kurdish forces had pulled back from the entire Turkish-Syrian border in accordance with a deal struck between Ankara and regime backer Moscow in Sochi earlier this month.
"The withdrawal of armed units from a territory where a security corridor should be created has been completed ahead of time," Shoigu said, as quoted by Russian news agencies.
The Turkish military and its Syrian proxies launched an offensive against Kurdish forces in northeastern Syria on October 9 with the aim of creating a buffer zone roughly 30 kilometres deep.
Earlier this month, Kurdish forces agreed to withdraw from a 120-kilometre long, Arab-majority segment of the 440-kilometre border zone, but clashes have been reported since.
The Turkish presidency said joint Turkish-Russian patrols - also planned under the Sochi deal - would verify the Kurdish forces' withdrawal.
Shoigu said Syrian border guards and Russian military police had been deployed in the area. But the situation was complicated by clashes between Syrian and Turkish forces on Tuesday.
The Britain-based Syrian Observatory for Human Rights reported that "heavy fighting erupted for the first time between the Syrian and Turkish armies", adding that six Syrian soldiers were killed near the key border town of Ras al-Ain.
"Turkish artillery fire killed five regime forces in battles on the edge of the village of Assadiya," Rami Abdel Rahman, the head of the Observatory, told AFP.
He added that Syrian fighters used by Turkey as the main ground force for the invasion had executed a government soldier they had captured. Later Tuesday, the Observatory reported more clashes between regime forces and Turkey's Syrian proxies.
Left in the lurch after US troops withdrew from the border area, Kurdish forces turned to the Syrian government for protection.
The regime's forces moved quickly north and are now expected to deploy along much of the border zone.
Turkish-Russian patrols in a 10-kilometre-deep strip on the border were to start, but strikes near the border town of Derbasiyeh threatened that deadline, both the Observatory and Syrian state media reported.
The Observatory said Turkish and Russian military units had been due to meet at a border crossing to discuss the upcoming patrols.
Syrian state news agency SANA reported "Turkish mortar fire on the Derbasiyeh border crossing", some 60 kilometres east of Ras al-Ain, and said six Syrian civilians had been wounded. It added that rounds were fired as Russian military police were driving by.
Turkey said the joint patrols with Russia would start "soon".
It said it would not hesitate to resume operations if it identified Kurdish fighters near the border after its defence ministry said it had arrested 18 who claimed to be regime forces near Ras al-Ain.
The Syrian Democratic Forces, the de facto army of the moribund autonomous Kurdish administrated territory, have voiced reservations over the Sochi deal.
The agreement, to which the Kurds are not signatories, essentially hands much of their heartland to the regime.
The United States allied with the SDF in 2014 to fight the Syrian side of the war against the militant Islamic State's then sprawling "caliphate".
That phase of the conflict ended in March this year with the demise of the IS proto-state's last bastion in eastern Syria and US President Donald Trump's indications that he wanted to pull American troops out of the Syrian quagmire.
US forces present as part of an anti-IS coalition had been acting as a buffer between Turkey and the Kurds, both theoretically US allies, but that ended when they pulled back from the border at the beginning of October.
The White House then announced US forces were leaving the country altogether but they have since redeployed further east around oil wells in areas still under Kurdish control.
"We want to keep the oil, and we'll work something out with the Kurds," Trump said. The Observatory said the US-led coalition Tuesday targeted regime positions in the eastern oil-rich province of Deir Ezzor with rocket fire.
The coalition did not immediately respond to a request for comment.
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