Fighting between Islamic State group jihadists and Kurdish militia in the key Syrian border town of Kobane has spread to new areas in the south and west, a monitor said on Tuesday.

The Syrian Observatory for Human Rights and an activist from the town also reported new air strikes by the 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 on Monday 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.

He said IS fighters had seized a number of buildings in the south and west of the town, including a hospital under construction on the western outskirts of Kobane.

Abdel Rahman also reported fresh air strikes by the US-led coalition overnight, saying they hit the east and southeastern edges of the town.

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.

"The Kurdish fighters are still optimistic, they only have light weapons, but they know Kobane well," he said.

"And they are fighting to defend their town and they say they will fight to the last person."

The Observatory said that at least 34 IS jihadists and 16 Kurdish fighters had been killed in Kobane in fighting on Monday.

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.