But a Kurdish journalist inside the town told AFP thousands of civilians had refused to abandon their homes.
Washington and its Arab allies stepped up air strikes on the advancing IS fighters -- AFP correspondents on the Turkish side of the border reported hearing at least eight around Kobane during the day.
The Pentagon said coalition strikes near Kobane on Monday and Tuesday had damaged or destroyed several armed vehicles, anti-aircraft artillery, a tank and a jihadist "unit".
But they failed to stop IS fighters from penetrating eastern neighbourhoods of the town on Monday, sparking fierce street battles with the Kurdish defenders.
The Syrian Observatory for Human Rights, a Britain-based monitoring group, said the Kurds had succeeded in forcing the jihadists to fall back in some areas they had entered.
But Turkish President Recep Tayyip Erdogan warned that the town was "about to fall", saying a ground operation was needed to defeat the militants.
"I am telling the West -- dropping bombs from the air will not provide a solution," he said.
Turkey last week won parliamentary approval for military intervention against IS in Syria and Iraq, but it has yet to announce any firm plans despite the advance of the jihadists on its doorstep.
Pro-Kurdish demonstrators angered by Turkey's lack of action clashed with police across the country Tuesday, leading to at least three deaths and several people wounded.
There were also protests in the Kurdish diaspora in Europe, with dozens of Kurdish demonstrators bursting into the European Parliament in Brussels.
- 'Need to act now' -
UN envoy to Syria Staffan de Mistura appealed to the international community to act immediately to defend the town against the much better armed IS fighters, who seized large amounts of heavy weaponry from retreating troops in a lightning offensive in neighbouring Iraq in June.
"The world, all of us, will regret deeply if (IS) is able to take over a city which has defended itself with courage but is close to not being able to do so. We need to act now," he said.
"The international community needs to defend them. The international community cannot sustain another city falling under (IS)".
Iran, which unlike the West supports President Bashar al-Assad's regime, criticised the "passivity of the international community" in the face of the IS offensive.
But analysts warned that a lack of ground support for air strikes against IS, and Turkey's reluctance to step in militarily, had all but sealed Kobane's fate.
"It is practically too late to save Kobane at this stage," said Mario Abou Zeid, a Beirut-based analyst with the Carnegie Middle East Centre.
The United States and its allies have launched nearly 2,000 air raids against jihadists in both Iraq and Syria in an attempt to stop their advance.
But Abou Zeid said: "The expansion of Islamic State forces in Kobane is new proof that the air strikes campaign is failing to achieve its objective."
Kobane, also known as Ain al-Arab, would be a major prize for the jihadists, as it would give them unbroken control of a long stretch of Syria's border with Turkey.
- 'Fight to the last' -
At least 412 people, more than half of them jihadists, have been killed in and around Kobane since IS began its assault in mid-September, according to the Observatory.
The defenders have vowed to "fight to the last person," said Kobane activist Mustafa Ebdi.
Kurdish journalist Ozgur Amed said there were thousands of civilians still inside the town. "They don't want to become refugees," he said.
"Our morale is still good," he told AFP by telephone from inside Kobane. "We are just afraid of the humanitarian situation getting worse."
White House spokesman Josh Earnest told reporters that Washington was "very concerned" about the safety of innocent civilians in the town.
"Once again, we are seeing this extremist organisation, in the name of an otherwise peaceful religion, Islam, perpetrating terrible acts of violence against religious and ethnic minorities."
"This is something we remain concerned about."
IS has been accused of carrying out widespread atrocities, including mass executions, abductions, torture and forcing women into slavery, with ethnic and religious minorities a particular target.