At the same time, Kobane district chief Anwar Muslim, said US-led air strikes had destroyed many Islamic State group vehicles and artillery pieces, and that the town's defenders are reinforcing their positions.
"There are civilians trapped in the centre and south of town, whom we cannot evacuate because of snipers and mortar fire," Muslim told AFP.
"Their situation is difficult."
There are no precise figures on how many non-combattants remain in Kobane, also known as Ain al-Arab.
Last week, the United Nations spoke of as many as 700, mostly elderly, civilians being trapped in the centre of the town. Another 10,000-13,000 were said to be gathered near the Turkish border.
For its part, the Britain-based Syrian Observatory for Human Rights says there are hundreds of civilians in the centre and west of town and that many of them refuse to leave, preferring to die than go into exile.
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The IS jihadists, who have seized swathes of Syria and neighbouring Iraq and declared a "caliphate," first attacked Kobane on September 16 in a bid to seal their control of a long stretch on the Syrian side of the border.
They succeeded in taking nearly half the town before its defenders, aided by US-led air strikes, began pushing them back.
Describing the situation Friday, Muslim said "you can see their bodies (IS jihadists) in the streets... Our forces are reinforcing their defensive positions."
The IS fighters are "mostly in the east and south, and have hidden their Hummers, artillery and tanks among the houses so as not to be targeted by the air strikes."
He saluted what he called the "incredible resistance" of Kobane's defenders, adding that the situation is still dangerous and that there is "no other choice but to resist."