IS militants advanced in the strategic town overnight despite intensified US air strikes, as calls grew for ground action to support Kobane's beleaguered Kurdish defenders.
But after talks with NATO chief Jens Stoltenberg, Turkish Foreign Minister Mevlut Cavusoglu said Ankara could not be expected to act alone.
"It's not realistic to expect that Turkey will lead a ground operation on its own," he said.
Kobane, whose Kurdish defenders have been holding out against a three-week siege by the jihadists, has become a crucial battleground and symbol of resistance to IS.
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Nearly 20 coalition bombing raids have hit near Kobane since Tuesday, but Washington has said air strikes alone would not be enough to save it.
Turkey has come under fire for its inaction as the jihadists advance on its doorstep, with protests in Kurdish areas sparking clashes that claimed at least 22 lives and forced authorities to declare a curfew in six provinces.
Fierce street battles have been raging in Kobane since the jihadists breached its defences earlier this week.
"Despite fierce resistance from the Kurdish forces, IS advanced during the night and controls more than a third of Kobane," Rami Abdel Rahman, director of the Syrian Observatory for Human Rights, told AFP.
US and coalition aircraft targeted IS fighters near the town yesterday, launching 14 attacks, the US military said.
The strikes destroyed five armed vehicles, an IS supply depot, a command centre, a logistics compound, and eight occupied barracks, Central Command said.
Kobane, also known as Ain al-Arab, would be a major prize for the jihadists, giving them unbroken control of a long stretch of Syria's border with Turkey.