The defenders of the Syrian Kurdish town claim to have repulsed waves of attacks by Islamic State militants, as pressure grows on Turkey to intervene.
The US military hit Islamic State (IS) militants with five air strikes on Wednesday and Thursday, sending huge plumes of smoke billowing above Kobani.
Turkey has ruled out a ground assault and its tanks are standing by while the town’s lightly-armed Kurdish defenders face IS attacks from three sides.
There are fears of a massacre if the Sunni Islamist group takes the Kurdish enclave, and victory would give IS control of a long uninterrupted swathe of territory along the Syrian/Turkish border.
Speaking to Channel 4 News from the centre of Kobani, Kurdish activist Khaled Barkal said IS were still bombing in many areas and tried to storm the town from several districts, but Kurdish YPG fighters pushed them back, forcing some Islamists to flee.
He said the morale of the Kurdish fighters was “very high” and that some young men had managed to cross over from the nearby border with Turkey to bolster the defences, despite a heavy Turkish security presence along the border.
Mr Barkal said the YPG had not received any cross-border military help, but one truck containing humanitarian aid like food and water made it through to the front line today.
In a press release on Thursday, the YPG claimed to have repulsed multiple IS attacks on three fronts, killing as many as 60 Islamists for the loss of nine of their own fighters. The claims could not be independently verified.
Amateur video posted on social media purports to show Arabic fighters from the Free Syrian Army attacking IS positions in Kobani in support of the YPG.
Kurds have demonstrated in cities across Turkey, in Kurdish northern Iraq and around Europe, calling for more military help for the Syrian Kurdish fighters, after both America and Britain said air strikes alone would not be enough to defeat the IS advance.
The US Central Command (Centcom) said the US military carried out five air strikes on Wednesday and Thursday, damaging an IS training camp, support buildings and two vehicles. They also hit one small and one large unit of fighters, it added.
Centcom said in a statement on Thursday that Kurdish militia appear to control most of Kobani and “are holding out” against IS.
Esmat al-Sheikh, head of the Kurdish militia in Kobani, said IS had seized about a quarter of the town in the east, saying: “The clashes are ongoing – street battles.”
Rami Abdulrahman from the Syrian Observatory for Human Rights monitoring group said fighters the Islamic State (IS) group “control more than a third of Kobani – all eastern areas, a small part of the northeast and an area in the south east.”
IS hoisted its black flag inside the town overnight as eyewitnesses reported hearing explosions and sporadic gunfire.
The foreign secretary, Philip Hammond, told the BBC: “The US has implemented some additional air strikes to try and help the people who are defending Kobani but it is a very difficult situation on the ground and we have never envisaged that the coalition’s intervention with air power in this battle was going to turn the tide in the short term.
“We have got to degrade Isil’s military capability over time, that isn’t going to happen overnight.
“So I don’t want to suggest that there is anything readily that the coalition can do that will make a fundamental difference on the ground in this battle, in the tactical situation that’s faced around Kobani.”
His words were echoed by US secretary of state John Kerry, who said: “As horrific as it is to watch in real time what is happening in Kobani … you have to step back and understand the strategic objective.”
Air strikes alone are not going to do this. They’re not going to fix this. John Kirby
A Pentagon spokesman, Rear Admiral John Kirby, told a press conference: “Air strikes alone are not going to do this. They’re not going to fix this. They’re not going to save the town of Kobani. We know that.”
He added: “In Syria, right now we just don’t have a ground force that we can work with.”
US President Barack Obama has ruled out using ground troops in the fight against IS, and plans to train Syrian rebels to take on the Islamists will take months, Mr Kirby said.
He warned that IS “is going to continue to grab ground and there are going to continue to be villages and towns and cities that they take”.
While the US is working with Kurdish peshmerga forces in northern Iraq, the defenders of Kobani are aligned with the PKK, a Kurdish separatist party designated a terrorist group by Turkey and the US.
The New York Times quoted an anonymous senior US official as saying that Washington was pressing Turkey to send troops across the border and carry out airstrikes of their own against IS.
But the Turkish foreign minister, Mevlut Cavusoglu, said: “It is not realistic to expect Turkey to conduct a ground operation on its own. We are holding talks…. Once there is a common decision, Turkey will not hold back away from playing its part.”
At least 21 people died on Wednesday as Kurdish demonstrators clashed with Turkish security forces in cities across the country.
Abdullah Ocalan, the jailed leader of the Kurdish militant group the PKK, has said a massacre of Kurds in Kobani would spell the end of a fragile peace process between Kurdish militants and the Turkish authorities.
But the United Nations says only a few hundred inhabitants remain in Kobani after hundreds of thousands of civilians fled over the border into Turkey.
Kurds at the Turkish-Syrian border cheered air strikes and protested that the Turkish authorities will not let them cross into Syria to join the fight.
Eyup Zencioglu said: “We are Kurdish. We are here to the death. They should give us permission to cross or the Turkish military should intervene with a ground operation.”
Mr Hammond said Britain could extend air strikes to Syria if the US-led coalitions asks for more air support. Ministers have said they will seek another vote in parliament if UK jets are asked to bomb IS positions in Syria as well as Iraq.
The foreign secretary said: “We absolutely have not ruled out playing a role in Syria.
“We will require further parliamentary approval if we decide that that is the right thing for us to do.
“We would see this as a military question – is there a militarily useful role that UK assets could play. If Centcom commanders see a specific role for UK military assets I am sure that they will not be slow in requesting them.”