The breakthrough saw IS claim half of Kobane, nearly a month after the Sunni extremists began their assault on the town on the Turkish frontier, despite more than three weeks of US-led air strikes in Syria aimed at stopping them.
That failure will be among the main points up for discussion at Tuesday's meeting in Washington of military chiefs from the 21 countries in the US-led coalition, as will Turkey's call for the establishment of a protective buffer zone.
A Kobane politician who is now a refugee said IS fighters had surrounded Kobane to the south, east and west, and warned of a "massacre" if they take the northern front bordering Turkey.
"If they manage to take control of that area, they will close all access to the town and will begin a massacre," Feyza Abdi said from Turkey.
"That is what they want, to completely enclose the town, cut off all contact with Turkey and engage in barbarism."
The Britain-based monitoring group later said IS had advanced into central Kobane, seizing a major building and squeezing the town's Kurdish defenders into its northern half bordering Turkey.
With the jihadists advancing on its doorstep, NATO member Turkey has come under intense pressure to take action as part of the coalition that has been carrying out air strikes in both Syria and Iraq.
Ankara, which has called for a buffer zone to guard its border and provide some protection to fleeing Kurds, denied allowing the United States to use its bases against IS.
But the Turkish government vehemently denied it was allowing US forces to carry out bombing raids from Incirlik.
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