The Syrian Observatory for Human Rights and an activist from the town also reported new air strikes by a US-led coalition against IS on the edges of the town overnight.
Observatory director Rami Abdel Rahman said street battles were now being fought in the south and west of Kobane, which is also known as Ain al-Arab, after IS jihadists entered it today evening.
"They have retreated by a few streets in the eastern areas they seized yesterday, but the fighting has now spread to the south and west of the town," Abdel Rahman said.
Abdel Rahman also reported fresh air strikes by the US-led coalition overnight, saying they hit the east and southeastern edges of the town.
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Kobane activist Mustafa Ebdi confirmed the strikes, but said they had little effect.
"The strikes hit the Mishtenur area," he said, referring to a plateau south of Kobane.
"But they (IS) aren't gathered there. There are other places they should be hitting," he said.
Ebdi confirmed street battles were being fought in the east, west and south of the town, which is bordered to the north by the Turkish border.
"And they are fighting to defend their town and they say they will fight to the last person."
IS jihadists began advancing on Kobane three weeks ago, quickly capturing a string of villages surrounding the town and prompting some 186,000 residents to flee into Turkey.
IS is hoping to seize the town to cement its grip over a long stretch of the border between Syria and Turkey.