At least 11 militants and four Kurdish fighters were killed in the fighting over Tel al-Shaer, a village on a strategic hill overlooking the town, Kurdish Rudaw news agency reported said.
Fighting between both sides continued until early Saturday in several areas on the outskirts of Kobane, the Syrian Observatory for Human Rights said.
The United States and allies have intensified their aerial campaign against the ISIS in Kobane after the radical group gained ground around the mostly Kurdish town in recent days.
The terrorist are thought to be trying to capture Mursitpinar, a border crossing into Turkey.
Capturing the crossing would preempt any reinforcements by Iraqi Kurds, who earlier this week voted to send reinforcements to Kobane.
Iraq's autonomous region of Kurdistan will dispatch the first 150 Peshmerga troops to Kobane on Sunday, Rudaw reported, citing unnamed military officials.
The Peshmerga - Kurdistan's official forces - will be equipped with heavy weapons in the fight against the Sunni extremists in Kobane, according to the Kurdish agency.
The ISIS also controls considerable swathes of territory in neighboring Iraq.