The Kurds claimed to have pushed IS back in parts of Kobane, but the Pentagon warned the multinational strikes may not prevent the town's fall even though hundreds of jihadists are thought to have been killed.
Mortar and heavy machinegun fire rang out later as IS appeared to have relaunched its bid to cut the town off from the Turkish border, said an AFP correspondent across the frontier.
"We need more air strikes, as well as weaponry and ammunition to fight them on the ground," said Idris Nassen, a Kurdish official in Kobane.
An estimated 200,000 mainly Kurdish Syrians have fled the IS onslaught for the relative safety of Turkey.
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A grocer who had escaped to Turkey from Kobane offered insight Thursday into those fighting for IS, saying that one they had captured, an Azerbaijani in his 20s, had even asked to be killed.
IS is also battling to control other parts of Syria, including Hasakeh province, where Kurdish fighters killed 20 jihadists Thursday, the Syrian Observatory for Human Rights said.
Kurdish forces have suffered heavy losses since IS launched its offensive on the Kurdish enclave around Kobane in mid-September, but so too have the jihadists.
As of Wednesday, ground clashes alone had killed 662 people since September 16, including 20 civilians, the Observatory said.
In its latest update, US Central Command said American warplanes struck 14 times near Kobane on Wednesday and Thursday, including "successful" raids on 19 IS-held buildings and two command posts.