The advance came hours after the US-led coalition launched four strikes against ISIL positions in central Kobani, according to the Syrian Observatory for Human Rights.
The Kurdish People's Protection Units (YPG) staged a "special operation" during which they captured six buildings used by ISIL, said the Britain-based group, which relies on a network of sources in Syria. Thirteen ISIL militants were killed, it said.
The Kurds "captured a large amount of weapons and ammunition, including RPG (rocket-propelled grenade) rounds, light weapons, sniper guns and thousands of heavy machine gun rounds," the Observatory said.
Highly motivated Syrian Kurdish troops are fighting alongside Iraqi peshmerga forces and Syrian rebels that have reinforced the town's defenses.