Kurdish commander pleads for help as Isis plant banner on hill overlooking Kobani and on a building in the town

The black flag of Isis was raised on the outskirts of the Kurdish Syrian town of Kobani on Monday afternoon as reports said Islamist fighters had advanced into the city after days of fighting.

From the Turkish border, the jihadi flag could be seen flying from a four-storey building on the east of the town close to the scene of some of the fiercest clashes. Moments later another flag was raised on a nearby hill.

Inside Kobani, known as Ain al‑Arab in Arabic, street battles raged between Kurdish fighters and the Isis force. The town and surrounding areas have been under attack since mid-September, with Isis militants capturing dozens of Kurdish villages. The assault has forced about 160,000 Syrians to flee and strained Kurdish forces, who have struggled to push back the extremists, despite being aided by US-led coalition air strikes.

The local government said thousands of Isis fighters were attacking the city centre, and issued a plea for international intervention.

“We are calling out to all international powers, forces from Kurdistan and Kurdish public that Isis thugs must be stopped and thousands of civilians must be saved from massacre,” the statement said.

A Kurdish commander told the Guardian by phone that the Isis flags were a ruse to sap morale among the defending force.

“I know they put an Isis flag on the hill. It is a lie. We want you to know they are not in the city right now. We would prefer to die than to leave Kobani,” said Ismat Sheikh Hassan, a commander of a Kurdish militia, the YPG.

But Parwer Ali Mohamed, a translator for the Kurdish Democratic Union party (PYD), told Reuters more than 2,000 people had fled the city to escape the fighting. “We can hear the sound of clashes on the street,” he said.

According to the UK-based Syrian Observatory for Human Rights, which monitors the war through a network of sources on the ground, Isis fighters had penetrated about 100 metres into the eastern part of the town.

“The battle has become street fighting, it is happening inside the town, the eastern part of the town,” the Observatory’s Rami Abdelrahman said.

Commander Hassan acknowledged there had been some action from the US-led coalition to strike Isis closer to Kobani, but he could not confirm whether it would be enough to force the jihadis back.

“Yesterday evening there were two bombs [dropped] behind the hill, but we don’t know if they did anything. And we still don’t have any other support,” he said.

The Turkish army has pushed Kurdish crowds away from its own side of the border with tear gas

“We are fighting against very heavy weapons and we haven’t got big weapons. We have limited weapons but they have big tanks, big bombs.

“Please show this to the whole world for the world to realise we are fighting with a very strong organisation. We need help,” he said.

Dozens of combatants on both sides were reported to have been killed in Sunday’s fighting, including a Kurdish peshmerga fighter who blew herself up, killing several jihadis.

Crowds gathered along the Turkish border, about 3km from the town, where the crackle of gunfire sounded closer than it has done in the past 22 days of fighting.

Stray shells continued to fall inside Turkish territory. Two more clusters of homes were evacuated on the Turkish side of the border while the army lined up at least 20 tanks on a hill to the west of Kobani, facing the border.

Isis flag outside Kobani. Photograph: Umit Bektas/Reuters

Kurds have come from all over Turkey to witness the fight for Kobani. Huseyin Icin, who works in human rights in the city of Izmir, said he had come to the border to see what he can do to help.

“We have a lot of relatives there: uncles, grandmothers, children, so we have to help each other. Isis is a very wild and strong terrorist organisation,” he said.

Icin echoed a common belief that Turkish security forces are supporting Isis, if only by preventing Kurdish fighters from crossing the border to fight.

“My relatives are there coming under fire from bombs, from tanks, from war, and here is the Turkish tanks and army and they’re not letting us do anything. They only want us to go there to take their corpses,” he said.

One Kurdish woman from the town of Suruc said: “If Isis takes Kobani, all of us will die. If they take that city, they will come here. And if Kobani is taken we will have just two options: we will kill them or they will kill us.