Kurdish fighters have thwarted an advance by the Islamic State of Iraq and the Levant (ISIL) into the heart of the besieged Syrian town of Kobane, according to a monitoring group.

Syrian Kurdish fighters reportedly pushed back an ISIL attempt to storm the centre of the town on Saturday, sparking 90 minutes of heavy clashes, the UK-based Syrian Observatory for Human Rights said on Saturday.

The Kurdish People's Protection Unit, known by its Kurdish initials YPG, told Al Jazeera that clashes were still raging in the eastern and southern parts of Kobane with no major advance from either side.

Al Jazeera's Stefannie Dekker, reporting from Buyuk Kendirli on the Turkey-Syria border, said the fighting had evolved into guerrilla warfare, sparking street-to-street battles between the Kurds and ISIL.

ISIL's pre-dawn attack on Saturday came a day after the armed group overran the Kurdish headquarters in the border town, sparking fears they would cut off the last escape route to neighbouring Turkey.

US-led coalition jets also carried out six air strikes on ISIL positions on Friday and Saturday, destroying a staging building, two small units, three lorries and damaging a command and control facility, the US Central Command said.

The strikes, which are aimed at rolling back gains by ISIL, appear to have done little to blunt its onslaught on Kobane that began in mid-September.

Since ISIL launched their offensive on Kobane, at least 500 people have been killed and more than 200,000 have been forced to flee across the border into Turkey.

On Friday, the UN envoy for Syria, Staffan de Mistura, warned that about 12,000 civilians were still in or near Kobane and were at risk of being "massacred".

The number included around 700 mainly elderly people in the town centre.