Fighting has reached the eastern outskirts of Kobane where Isis fighters raised their black flag over a 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 3000 civilians are believed still to be in Kobane, 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, killing 10 jihadists. She had stayed behind as Kurdish forces withdrew and mingled with the attackers before detonating explosives.
The battle for Kobane 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 northern 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 Isis "is saying that 'we can still win victories on the ground' and the capture of Kobane will give them complete control over territory stretching from Mosul to Aleppo".
He said that Turkey had used the desperation of the Kurds in Kobane to extract political concessions from them before allowing reinforcements and supplies to reach up to 3000 fighters of the People's Protection Units (YPG) who are holding the town.
The fall of Kobane would be a bad blow to the US and its anti-Isis coalition which has been bombing Isis positions in Syria since September 23 and in Iraq since August 8.
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 Monday in which 74 Isis fighters, as well as 15 Kurdish militiamen, were killed.
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".
Kobane 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 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.
Choppers strike
United States forces have begun air strikes using helicopter gunships assigned to protect the US Embassy in Baghdad. The strikes, believed to involve Apache helicopters, started amid heavy fighting against Isis in the western approaches to Baghdad, around Fallujah and Hit. Dr Afzal Ashraf, a defence expert at the Royal United Services Institute, said the Apaches were a more appropriate aircraft to back up the Iraqi forces. He said: "It's much better to use Apaches than fast jets because you can get up close and have time for a target to pop up. Then you can use machine guns, rather than a big 500lb bomb that can cause a lot of civilian damage."
Isis flag flies
The black flag of Isis was flying over Kobane in Syria despite US and coalition efforts to defend the town with air strikes. The town, on the border with Turkey, has been under jihadist attack for more than three weeks and the Islamist fighters have entered it. After Isis flags were flown from the top of buildings at the eastern entrance to the town, the battle moved from one of shellfire to urban warfare. "We can hear the sound of clashes in the street," said Parwer Ali Mohamed, a translator for the Kurdish Democratic Union party.
Nato poised
The Nato alliance has drawn up a strategy to defend Turkey if it is attacked along its border with Syria. Turkish Defence Minister Ismet Yilmaz said the alliance did that at his Government's request. "If there is an attack, Nato's joint defence mechanisms will be activated," Yilmaz said. Under Nato rules, an attack against one member is considered an attack against all alliance members.
Aussies get ready
Australian special forces are ready to start work in Iraq as soon as the paperwork is done. Prime Minister Tony Abbott said Australia was finalising the legal documentation that gave authority for special forces soldiers to help support and train Iraqi troops.
- Telegraph Group Ltd, AAP, AP