Isis is close to capturing the Syrian Kurdish town of Kobani, just a short distance from the Turkish border, after a three-week siege in which US air strikes turned out to be ineffective in preventing Isis winning an important victory.

With Isis fighters also making advances into western Baghdad, which may allow them to close the city’s airport with artillery fire, President Obama’s strategy of containing the Islamic militants in Iraq and Syria is in ruins.

Kurdish militiamen are battling to stop Isis capturing Kobani, but a Kurdish spokesman in the city was quoted as saying that the town “will certainly fall soon”. Fighting has reached the eastern outskirts of Kobani where Isis fighters raised their black flag over one building at the entrance to the town.

Earlier the Kurds claimed a success when they drove Isis fighters from high ground overlooking the city called Mishtenur hill, but they appear to have lost it again. Some 3,000 civilians are believed still to be in Kobani, while 160,000 of its people have already fled.

A Kurdish female fighter called Deilar Kanj Khamis, better known by her military name, Arin Mirkan, blew herself up in the course of the fighting on Sunday, killing 10 jihadists. She had stayed behind as Kurdish forces withdrew and mingled with the attackers before detonating explosives.

The battle for Kobani has united Kurds across the region who see it as their version of the battle of Thermopylae, with their heroic soldiers fighting to the end against Isis forces superior in numbers and armed with heavier weapons.

Isis is using tanks and artillery it seized from the Iraqi and Syrian armies when it overran their bases during the summer.

Isis forces have also captured Hit in Anbar province and parts of the provincial capital Ramadi.

The successful advance of the militants shows that the Iraqi army is little more capable of resisting Isis than when it lost Mosul and Tikrit in June.

The ability of Isis to resume offensive operations may also be a sign that the effectiveness of US air power, without highly trained observers on the ground to call in air strikes, is limited when used against well-led forces.

A veteran Kurdish leader, Omar Sheikhmous, said that Isis “is saying that ‘we can still win victories on the ground’ and the capture of Kobani will give them complete control over territory stretching from Mosul to Aleppo.”

Isis fighters in Kobani (2014): Civilians flee as militants enter Syria-Turkey border Show all 22 1 /22 Isis fighters in Kobani (2014): Civilians flee as militants enter Syria-Turkey border Isis fighters in Kobani (2014): Civilians flee as militants enter Syria-Turkey border Syria-Turkey border Mourners gathered to bury three Kurdish fighters from Kobani Isis fighters in Kobani (2014): Civilians flee as militants enter Syria-Turkey border Syria-Turkey border An explosion rocks the Syrian city of Kobani during a reported suicide car bomb attack by Isis Getty Isis fighters in Kobani (2014): Civilians flee as militants enter Syria-Turkey border Syria-Turkey border The US and Turkey have stepped up support for Kurdish fighters defending Kobani against Isis but it is still feared the town may fall; above, observers watch the fighting from a nearby village AFP Isis fighters in Kobani (2014): Civilians flee as militants enter Syria-Turkey border Syria-Turkey border People are silhouetted on the top of a hill close to the border line between Turkey and Syria near Mursitpinar bordergate as they watch the U.S led airstrikes over ther Syrian town of Kobani Isis fighters in Kobani (2014): Civilians flee as militants enter Syria-Turkey border Syria-Turkey border Syrian Kurd Kiymet Ergun (56) gestures, in Mursitpinar on the outskirts of Suruc, at the Turkey-Syria border, as thick smoke rises following an airstrike by the US-led coalition in Kobani, as fighting continued between Syrian Kurds and the militants of Isis group Isis fighters in Kobani (2014): Civilians flee as militants enter Syria-Turkey border Syria-Turkey border Kurdish Rabia Ali (R) accompanied by her son Ali Mehmud (L) mourn at the grave of her son Seydo Mehmud 'Curo', a Kurdish fighter, who was killed in the fighting with the militants of the Islamic State group in Kobani, and was buried at a cemetery in Suruc, on the Turkey-Syria border Isis fighters in Kobani (2014): Civilians flee as militants enter Syria-Turkey border Syria-Turkey border Mourners gather for the funeral of two Syrian Kurdish fighters killed in fighting with militants of the Isis group in Kobani at a cemetery in Suruc Isis fighters in Kobani (2014): Civilians flee as militants enter Syria-Turkey border Syria-Turkey border Kurdish refugees fleeing Kobani enter Turkey at Suruc Getty Images Isis fighters in Kobani (2014): Civilians flee as militants enter Syria-Turkey border Syria-Turkey border Smoke from air strikes against Isis in Kobani can be seen from across the border in Mursitpinar, Turkey Getty Images Isis fighters in Kobani (2014): Civilians flee as militants enter Syria-Turkey border Syria-Turkey border Newly arrived Kurdish refugees after crossing into Turkey from the Syrian border town of Kobani Getty Images Isis fighters in Kobani (2014): Civilians flee as militants enter Syria-Turkey border Syria-Turkey border Kurdish refugees cross the border near Kobani Getty Images Isis fighters in Kobani (2014): Civilians flee as militants enter Syria-Turkey border Syria-Turkey border Smoke rises from the city centre of Kobani Getty Images Isis fighters in Kobani (2014): Civilians flee as militants enter Syria-Turkey border Syria-Turkey border Isis militants stand next to an Isis flag atop a hill in the Syrian town of Ain al-Arab, known as Kobani by the Kurds, as seen from the Turkish-Syrian border, with Turkish troops in foreground, in the southeastern town of Suruc, Sanliurfa province Isis fighters in Kobani (2014): Civilians flee as militants enter Syria-Turkey border Syria-Turkey border A flag of Isis group is seen atop of a building at the eastern side of the town of Kobani, Syria, where fighting had been intensified between Syrian Kurds and the militants of Isis group Isis fighters in Kobani (2014): Civilians flee as militants enter Syria-Turkey border Syria-Turkey border Militants with the Isis group are seen after placing their group's flag on a hilltop at the eastern side of the town of Kobani Isis fighters in Kobani (2014): Civilians flee as militants enter Syria-Turkey border Syria-Turkey border Smoke rises after an apparent airstrike by allied forces against Isis targets in the west of Kobani where Kurdish fighters try to defend the town, near Suruc district, Sanliurfa, Turkey Isis fighters in Kobani (2014): Civilians flee as militants enter Syria-Turkey border Syria-Turkey border Newly arrived Syrian Kurdish refugees stand at the back of a truck after crossing into Turkey from the Syrian border town Kobani, near the southeastern Turkish town of Suruc in Sanliurfa province Isis fighters in Kobani (2014): Civilians flee as militants enter Syria-Turkey border Syria-Turkey border Turkish forces fire tear gas to disperse Kurds on the outskirts of Suruc, at the Turkey-Syria border, as fighting intensified between Syrian Kurds and the militants of Isis in Kobani Isis fighters in Kobani (2014): Civilians flee as militants enter Syria-Turkey border Syria-Turkey border Kurdish men shout towards Turkish army soldiers, who try to evacuate people from the village of Mursitpinar, on the other side of the Syrian town of Ain al-Arab, known as Kobani by the Kurds, by the Turkish-Syrian border in Sanliurfa province Isis fighters in Kobani (2014): Civilians flee as militants enter Syria-Turkey border Syria-Turkey border Turkish Kurds walk as tanks in the background hold their positions on a hilltop in the outskirts of Suruc, at the Turkey-Syria border, overlooking Kobani in Syria where fighting had ben intensified between Syrian Kurds and the militants of Isis Isis fighters in Kobani (2014): Civilians flee as militants enter Syria-Turkey border Syria-Turkey border Turkish Gendarmerie use tear gas to disperse Kurdish protesters during a demonstration against the Isis, at the Syria-Turkey border near Sanliurfa Isis fighters in Kobani (2014): Civilians flee as militants enter Syria-Turkey border Syria-Turkey border Smoke rises from the Syrian town of Ain al-Arab, on the Turkish-Syrian border in the southeastern town of Suruc, Sanliurfa province

He said that Turkey had used the desperation of the Kurds in Kobani to extract political concessions from them before allowing reinforcements and supplies to reach the 2,000 to 3,000 fighters of the People’s Protection Units (YPG) who are holding the town.

The fall of Kobani would be a bad blow to the US and its anti-Isis coalition which has been bombing Isis positions in Syria since 23 September and in Iraq since 8 August.

But in both countries Isis is still on the offensive and is making gains in Anbar province in western Iraq and in towns close to Baghdad. Isis fighters have responded to air attacks by spreading out so they are difficult to find and target.

The YPG said that there were 50 clashes with the enemy on Sunday in which 74 Isis fighters, as well as 15 Kurdish militiamen, were killed.

Mr Sheikhmous said that, unlike the situation in Sinjar in Iraq, where Kurdish villages were overrun before their inhabitants could flee, the Kurdish local authorities had told civilians “to flee from their villages into Turkey because they could not defend them”.

Kobani is one of three Kurdish cantons on the Syrian side of the Turkish border where many of Syria’s two-and-a-half million Kurds live.

President Bashar al-Assad withdrew his forces from these enclaves earlier in the war, leaving them in the hands of the Democratic Unity Party (PYD) whose militia is the YPG. Both are effectively the Syrian branch of the PKK that has been fighting for Kurdish self-rule in Turkey since 1984.

The long-running peace process between the PKK and the Turkish government could be one casualty of the fall of Kobani. Turkish forces have done nothing to help the Syrian Kurds hold the town and there is no sign of powerful Turkish military forces along the border intervening.

The leader of the PYD, Salih Muslim, is reported to have met officials from Turkish military intelligence to plead for aid but was told this would only be available if the Syrian Kurds abandoned their claim for self-determination, gave up their self-governing cantons, and agreed to a Turkish buffer zone inside Syria. Mr Muslim turned down the demands and returned to Kobani.

President Recep Tayyip Erdogan has been expressing outrage that the US Vice-President Joe Biden should have identified Turkey, Saudi Arabia and the United Arab Emirates as the states whose military and financial support led to the growth of Isis and Jabhat al-Nusra.

Mr Biden told a meeting at Harvard University’s Institute of Politics on 2 October that the Turks, Saudis and UAE “poured hundreds of millions of dollars and tens of thousands of tons of weapons against anyone who would fight Assad, except that the people who were being supplied were al-Nusra and al-Qaeda and the extremist element of jihadis coming from other parts of the world.”