The offensive, launched late on Saturday, is aimed at retaking the town of Tal Hamis and areas around it that are under the control of the Islamic State group, the Syrian Observatory for Human Rights said.
Kurdish militia forces, known as the People's Protection Units (YPG), "managed to advance and took over some 20 villages, farms and hamlets in the area," the Britain-based Observatory said.
At least 12 jihadists were killed in the fighting, it said. It was not known if Kurdish forces lost any fighters.
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Warplanes from the US-led coalition against IS carried out several strikes targeting jihadist positions in the area during the fighting, the Observatory said.
Newaf Khalil, a spokesman for the Kurdish Democratic Union Party (PYD), confirmed the advance and said fighting was raging in the area.
"This is one of the YPG's biggest recent operations," Khalil said.
The offensive began nearly a month after the YPG recaptured all of the town of Kobane on the border with Turkey from IS, after four months of fierce fighting backed by Syrian rebels and US-led coalition air strikes.