Nine Kurdish fighters of the People's Protection Units (YPG) and one IS militant died in the clashes around Ain-al-Arab on the border with Turkey, the Syrian Observatory for Human Rights said.
The militant are just two to three kilometres (a couple of miles) from the town, known as Kobane in Kurdish, said the Britain-based Observatory, which has a wide network of sources inside Syria.
Their offensive, launched just over two weeks ago, has sparked an exodus of tens of thousands of mainly Kurdish refugees into Turkey.
Kurdish leaders have appealed to the US-led coalition battling IS to provide air support to the town's defenders.
But the Observatory reported no coalition air or missile strikes in the area overnight.
Ain al-Arab would be a key prize for IS, giving it unbroken control of a long stretch of the Syrian-Turkish border.