Fresh air attacks by the US-led coalition have hit positions held by ISIL fighters in the southwest of the key Syrian border city of Kobane.

Tuesday's attacks came a day after ISIL pushed into Kobane, seizing three districts in the east and raising the group's black flags after fierce battles with its Syrian-Kurdish defenders.

Al Jazeera's Yilmaz Akinci, reporting from the Turkish border near Kobane on Tuesday, said that coalition air strikes had hit the centre of the city. 

Kobane in the firing line
If ISIL captures Kobane it will control three border crossings with Turkey and smuggling would become much easier. 

Kobane had a population of about 300,000 before ISIL attacking.

The majority are Kurds and have political affiliations with the Kurdistan Workers' Party.

The Kurds declared self-rule in January 2014 in areas which are now under attack by ISIL. 

On October 5, ISIL took over Tal Mashta al-Nour, a strategic hill which overlooks the town.

Turkey pledged to prevent Kobane from falling into ISIL and parliament authorised military operations.

"About 40 minutes after the air strikes, ISIL started to shell inside the city centre too," Akinci said.

Despite's ISIL's advances, the AFP news agency reported that a Kurdish flag could still be seen flying from a roof in the centre of the town.

Idris Nahsen, a Kurdish official still in Kobane, told AFP by telephone that ISIL was still trying hard to capture the city, but that resistance from fighters from the Kurdish YPG force had stopped their progress on Monday and last night.

The US-led coalition airstrikes, which continued in the night and the morning, are "helping but are not enough", he added, calling for arms and ammunition to be supplied to the Kurdish fighters.

Nahsen said the Kurds were in contact with both the US-led coalition and Turkey in search of more assistance.

"We need help from the international community. Either we finish them or they will finish us," he said.

The clashes are the heaviest since the start of the three-week offensive as ISIL tries to bring in more fighters to take control of the city.

Kobane has become a crucial battleground in the international fight against ISIL fighters. The battle has forced an estimated 186,000 civilians to flee to Turkey.

The Turkish parliament in Ankara last week authorised the government to join a US-led campaign against ISIL, but no plans for military action have been announced so far.

Al Jazeera's Bernard Smith, reporting from Urfa in Turkey, said that the country had found itself in an "incredibly difficult position".

"Turkey doesn't want to see an autonomous Kurdish-area on its border with Syria, while it doesn't want ISIL to be in power either. And it doesn't want Syrian president Bashar al-Assad to take control either," he said.

Smith said that Kurds were asking Turkey to allow more of its fighters into Syria, but "it doesn't want to see it backfire in the future".

Source: Al Jazeera and agencies