Fighters from the Islamic State of Iraq and the Levant (ISIL) group have reportedly withdrawn from some parts of the embattled Syrian city of Kobane overnight after air strikes by a US-led coalition.

Al Jazeera's Bernard Smith, reporting from the Syrian-Turkish border city of Urfa, said that Syrian-Kurdish fighters confirmed on Wednesday that the coalition airstrikes had "enabled them to push ISIL back towards the edges of the city from the areas that they had breached on Monday evening".

Smith added that the Syrian-Kurdish fighters felt that they were back on the offensive in the city, also known as Ain al-Arab.

Rami Abdel Rahman, director of the Syrian Observatory for Human Rights (SOHR), also said on Wednesday that ISIL had withdrawn overnight from several areas in the eastern and southwestern edges of Kobane.

After the pullback, ISIL fighters were still present in eastern parts of the strategic city and its southern edges, but were no longer inside on the western front, Abdel Rahman said.

He said that the move came after airstrikes had caused casualties and damaged at least four of their vehicles.

'Streets full of bodies'

On Tuesday, Turkish President Recep Tayyip Erdogan said that Kolbane was on the verge of falling to the armed group.

"Months have passed but no results have been achieved. Kobane is about to fall ... I am telling the West [that] dropping bombs from the air will not provide a solution," he said.

Erdogan said his country's military would stage a ground war against ISIL only if a buffer zone was set up between Turkey and Syria, and a no-fly zone over Syria along with the training and arming of moderate fighters battling against the Syrian President, Bashar al-Assad.

French President Francois Hollande said on Wednesday he backed the Turkish demand for a safe haven for Syrians.

At least 12 people were killed in Kurdish demonstrations across Turkey demanding the government to do more to protect Kobane from ISIL.

ISIL fighters entered Kobane on Monday night, after nearly three weeks of fighting around the city on the Syria-Turkey border.

On Tuesday, fighting raged in the east, west and south of Kobane, which is Syria's third biggest Kurdish city, and a US-led coalition fighting ISIL carried out multiple air strikes in and around the city.

Mustafa Ebdi, a Kurdish journalist and activist from Kobane, posted on his Facebook page that "the streets of the Maqtala neighbourhood in southeastern Kobane are full of the bodies of Daesh fighters," using the Arabic acronym for ISIL.

But he added that hundreds of civilians remained in the city and "the humanitarian situation is difficult and people need food and water".

Iraqi helicopter downed

ISIL began its advance on Kobane on September 16, quickly sweeping through the surrounding countryside and prompting an estimated 186,000 people to flee the region across the border into Turkey.

According to the SOHR, at least 412 people have been killed in the fighting, though the group said it believed the actual toll could be twice as high.

Meanwhile, ISIL fighters downed an Iraqi army helicopter near an oil refinery in Baiji, the control of which is split between the Iraqi army and ISIL.

Al Jazeera's Imran Khan, reporting from Baghdad, said this was the second Iraqi helicopter to be brought down within a 10-day period.

"[ISIL] captured air defence systems from the Iraqi army during their initial push. They have been using those, to a devastating effect as they say, within Baiji," said our correspondent.

Source: Al Jazeera and agencies