Turkish warplanes roared into northern Syria at daybreak and artillery pounded what security sources said were sites held by the Kurdish YPG militia, after the Syrian Observatory for Human Rights reported fierce overnight fighting around two villages.
Turkey said 25 Kurdish militants were killed in its air strikes and denied there were civilian casualties.
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There was no immediate comment from the YPG, but forces aligned with the group have said it had withdrawn from the area prior to the assault.
Turkey, which is also battling Kurdish insurgents at home, sent tanks and troops into Syria on Wednesday to support its Syrian rebel allies. The Turkish-backed forces first seized the Syrian border town of Jarablus from Islamic State militants before pushing south into areas held by Kurdish-aligned militias. They have also moved west towards Islamic State areas.
Turkish officials say their goal in Syria is as much about ensuring Kurdish forces do not expand the territory they already control along Turkey's border as it is about driving Islamic State from its strongholds.
However, the Turkish offensive has so far focused on forces allied to the Kurdish-backed Syrian Democratic Forces (SDF), a coalition that includes the YPG, an Observatory source said.
The SDF has support from the United States -- which sees the group as an effective Syrian ally against Islamic State, putting Turkey at odds with a fellow NATO member and further complicating Syria's five-year-old civil war.
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The conflict began as an uprising against Syrian President Bashar al-Assad and has since drawn in regional states and world powers.
Civilians killed, scores wounded
The Observatory, a Britain-based monitoring group with a network of sources in Syria, said Turkish-allied forces had seized at least two villages south of Jarablus, Jub al-Kousa and al-Amarna, that were held by militias loyal to the SDF.
The fighting killed 20 civilians in Jub al-Kousa and 15 in al-Amarna, while scores more were wounded, the group said.
Turkish-backed rebels said they had seized a string of villages south of Jarablus controlled by SDF-aligned forces and had moved west to take several villages held by Islamic State.
Turkish security sources said warplanes and artillery had hit YPG sites south of Jarablus and towards Manbij, a city captured by the SDF this month in a U.S.-backed operation.
Colonel Ahmed Osman, head of the Turkish-aligned Sultan Murad rebel group, told Reuters the force was "certainly heading in the direction of Manbij" and hoped to take it.
Ankara wants to stop Kurdish forces gaining control of an unbroken swathe of Syrian territory on Turkey's frontier, which it fears could embolden the Kurdish PKK militant group that has waged a three-decade insurgency in Turkey.
A Reuters witness in Karkamis, a Turkish border town, heard jets and artillery strike within Syria. A Turkish official told Reuters heavier air strikes could come in the hours ahead.
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Turkey said one of its soldiers was killed on Saturday when a rocket that it said came from a YPG-controlled area hit a tank. It was the first Turkish death reported in the campaign.
Turkey has suffered shock waves from the conflict raging in its southern neighbor, including bombings by Islamic State.
The government suspects the jihadist group was behind a blast at a wedding this month that killed 54 people in southeastern Turkey.
President Tayyip Erdogan struck a defiant note during a visit to the site of the wedding attack. "Our operations against terrorist organizations will continue until the end," he told a rally of thousands of supporters on Sunday.
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