The strategically located town on the border with Turkey has become a major symbol of resistance against IS, which has seized large parts of Syria and Iraq, committing widespread atrocities.
The jihadists launched a major offensive in mid-September to try to capture Kobane, and at one point controlled more than half of the town, known in Arabic as Ain al-Arab.
But supported by US-led air strikes and reinforced by Kurds from Iraq, "Kurdish forces now control more than 60 percent of the city", said Rami Abdel Rahman, director of the Britain-based Syrian Observatory for Human Rights.
"IS has even left areas that the Kurds did not enter for fear of mines," he added.
A Kurdish activist from Kobane, Mustefa Ebdi, said that Kurdish militia defending the town had advanced eastwards on the frontline during the past week.
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IS has withdrawn from the seized Kurdish militia headquarters in the north of the city, as well as from southern and central districts, according to activists.
"The Kurdish advance is due largely to the air strikes by the coalition," said Ebdi.
"The jihadists are now using tunnels after failing in their tactics of car bombs and explosive belts," he said.
Dozens of IS fighters have carried out suicide bomb attacks in Kobane in the face of fierce Kurdish resistance.
More than 1,000 people are reported to have been killed in the battle for the town, most of them jihadists.