The operation in Afrin - bordering Turkey's Hatay and Kilis provinces - was widely expected in the wake of Turkey's Operation Euphrates Shield in northern Syria, which cleared Daesh terrorists from Turkey's border between August 24, 2016, and March 2017.
"We are carrying out our struggle there determinedly and we will continue to do so".
If confirmed, Rajo would be the largest centre in Afrin to be captured since the Turkish offensive began on January 20. A Syrian territory controlled by Turkish-backed Syrian opposition fighters lies to the east.
Turkish troops and allied Syrian fighters have been attacking Afrin from the north, west and east, and have formed a crescent around the district.
Turkey's state-run Anadolu Agency (AA) reported that Turkish and FSA forces have liberated Haji Khalil, a village in Raju, Afrin, from the PPK-linked Democratic Union Party's (PYD) armed wing, People's Protection Units (YPG).
UA outside counsel releases statement on Deandre Ayton
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The truce does not apply to the Islamic State group, al-Qaeda and groups associated with it, or other groups deemed terrorist by the Security Council, and has also been ignored by the Syrian regime and Russian Federation in Eastern Ghouta.
The US has no troops in Afrin, but said it fears the Turkish offensive could distract from the fight against IS in the east.
Turkish warplanes struck pro-Syrian government forces in the northwestern Afrin region of Syria on Saturday, killing at least 36 of them, as Turkey's assault in the Kurdish region gathered pace, the Syrian Observatory for Human Rights said.
Later on Sunday, four more villages and a mountain were liberated.
The military said in a statement that the army had taken control of seven settlements including Rajo on Saturday. An elderly Pakistani couple managed to leave after negotiations.
Turkey launched Operation Olive Branch, its second military intervention in Syia since 2011, after Washington said it would set up a border force comprising 30,000 Kurdish militants near Turkish soil.
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