Outgunned Kurdish militia were struggling to prevent the jihadists closing off the last escape route for civilians still in the area, prompting an appeal yesterday for urgent military assistance.
US-led warplanes have intensified air strikes against IS, which has been attacking Kobane for three weeks, but the Pentagon has said that there are limits to what can be done without troops on the ground.
Washington also warned that the military campaign could lead to reprisal attacks "against US, Western and coalition partner interests throughout the world".
Four straight nights of protests among Turkey's large Kurdish minority have left 31 people dead as anger flared over the government's lack of action to save Kobane.
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IS now controls 40 percent of the town, according to the Britain-based Syrian Observatory for Human Rights.
As fighting raged, an IS suicide bomber struck to the west of the Kurdish headquarters in Kobane killing two people, and 10 Kurds were killed in an IS ambush on the south side of town, the Observatory said.
An AFP correspondent on the Turkish side of the border saw a cloud of white smoke rising above Kobane after coalition strikes yesterday.
UN envoy for Syria Staffan de Mistura warned that 12,000 or so civilians still in or near Kobane, including 700 mainly elderly people in the town centre, "will most likely be massacred" by IS if the town falls.
Kobane was "literally surrounded" except for one narrow entry and exit point to the border, de Mistura said.
The envoy called on Turkey, "if they can, to support the deterrent actions of the coalition through whatever means from their own territory."
The United States reported "progress" in pressing Turkey to participate in the fight against the Islamic State group, noting a pledge from Ankara to train and equip moderate Syrian rebels.