Syrian Kurdish fighters in Kobani told a monitoring group they have made further gains against Islamic State militants and now control 80 percent of the city.
The British-based Syrian Observatory for Human Rights said among areas retaken by Kurdish People's Protection Units, or YPG, is Kobani's security and government district.
YPG forces said they killed 14 Islamic State fighters in heavy fighting Sunday, adding most of them were non-Syrians.
The claims could not be independently confirmed. The clashes followed several airstrikes against Islamic State targets by the U.S.-led coalition in recent days.
Kobani, which lies on the border with Turkey, came under Islamic State siege in September and at various points appeared poised to fall to militant control. But coalition airstrikes and reinforcements from Kurdish fighters from Iraq helped push Islamic State fighters back.
The city, also known as Ain al-Arab, has been severely damaged by months of fighting, with some districts lying in ruin. Many of the town's civilians have sought refuge in Turkey.