Fierce fighting between Kurdish forces and fighters belonging to the Islamic State of Iraq and the Levant (ISIL) is continuing around the Syrian town of Kobane, sparking an exodus into nearby Turkey.

By Wednesday, about 140,000 Syrian Kurdish refugees had made their way into Turkey since the ISIL offensive on the town and its surrounding areas began on September 15.

Al Jazeera's Stefanie Dekker, reporting from the Turkish side of the border, said the tens of thousands had crossed the border since US-led strikes on ISIL targets began on Tuesday.

She said the Kurds had managed to put up a fight against ISIL, but had battled to compete with the self-declared jihadists' superior firepower and weaponry. 

"They say they have the men but not the weapons to defeat ISIL," our correspondent said.

Hundreds of Kurdish men who had crossed the border with their families were seeking to return across the border into Syria to help defend Kobane.

"People are saying that they are going back to protect their town and villages and they want to fight to push ISIL back ... The say that the air strikes are helpful but won't solve the issue," our correspondent said.

The developments on the border comes after at least 105 villages around Kobane were captured by ISIL fighters, including at least 85 over the weekend, UN human rights spokesman Rupert Colville said on Tuesday. 

Colville said he had reports that an additional 100 villages had been abandoned or evacuated for fear of being captured.

The UN refugee agency (UNHCR) said it was making contingency plans for all 400,000 inhabitants of Kobane to flee into Turkey.

The United States and its Arab allies bombed Syria for the first time on Tuesday, reportedly killing scores of ISIL fighters and members of a separate al-Qaeda-linked group.