Jihadists waged fierce street battles Tuesday with Kurdish militia backed by US-led air strikes in a Syrian border town whose fall would mark a major victory for the Islamic State (IS) group.

With the fight for Kobane entering a crucial phase, the IS jihadists fought to extend their foothold into new areas in the south and west of the town, a day after piercing its Kurdish defenses.

Kobane is seen as a strategic prize whose capture would give IS a long stretch of the border with Turkey for its self-proclaimed "Islamic caliphate," which already spans large parts of Syria and Iraq.

The IS jihadists "are trying hard to capture the city," Idris Nahsen, a Kurdish official still in Kobane, told AFP by telephone.

He said they were meeting resistance from the Kurdish People's Protection Units. The Kurds have repeatedly called for increased foreign military support.

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 across the Turkish border.

Turkey last week won parliamentary approval for military intervention against IS, but it has yet to announce any plans for military action.

IS has been accused of carrying out widespread atrocities, including mass executions, abductions, torture and forcing women into slavery.

The jihadists sparked fresh outrage at the weekend with the release of a video showing the beheading of British aid worker Alan Henning.

The video - the latest in a series of murders of Western hostages - also included a threat to US aid worker Peter Kassig.