Syrian Kurds have issued a desperate call for western powers and their own kin to rally to the defence of the city of Kobani, which appears closer than ever to falling in the face of a sustained barrage from Islamic State militants.

The city, one of the largest Kurdish bastions of resistance to Isis in northern Syria, was shaken by heavy shelling from the advancing militants at dusk on Friday, sending plumes of smoke skywards and more refugees scrambling across the border into Turkey. Isis fighters are believed to be inside the eastern part of the city now, where some of the heaviest clashes are reverberating.

“This is one of the strongest days of fighting we have seen,” said Ismet Sheikh Hasan, a commander with the YPG Kurdish force defending Kobani. “Isis is thinking that tomorrow is a very important day, Eid, so they took their tanks and members of Isis from Aleppo, from Raqqa, from the other cities nearby in order to conquer the mosque of Kobani.”

The frequent booms of the bombs and billows of smoke drew crowds from the nearby Turkish towns, who turned out to watch the battle play out on the hillside before them.

Hasan reiterated calls for international support for the city, but said they have thus far fallen on deaf ears. “We haven’t had any contact from the Turkish army up until now, and no help from the international forces either,” he told the Guardian.

The armed group also issued a statement calling on all Kurds to join the fight. “Our call to all the young men and women of Kurdistan ... is to come to be part of this resistance. Join the heroic [YPG], and take this resistance to the highest possible level,” it said.

After its parliament agreed to allow operations inside Syria and Iraq, Turkey has indicated it will do what it can to prevent Kobani from falling. But Syria has warned that any Turkish military intervention on its soil would be considered an act of aggression.

“The international community and, in particular, the security council, should act to put an end to the adventures of the Turkish leadership, which represents a threat to world security and peace,” the foreign ministry said.

If Kobani falls it would solidify Isis’s presence in northern Syria and give it a new springboard from which to extend its self-declared “state” westwards. It would also aggravate the refugee crisis across the border in Turkey. Tens of thousands have crossed the border in recent weeks from the Kobani enclave, swelling a refugee population already in excess of 1.3 million.

Kurdish forces have in recent days evacuated several villages around Kobani. According to local media, Isis took the strategically crucial Zorova Hill to the west of Kobani back from Kurdish YPG forces late on Thursday night. Sources in the Kurdish Democratic Union party, the political wing of the YPG, announced that fighters had retreated to the city to prepare for “guerrilla-style urban warfare”.

In Kobani itself, the mood appeared to be defiant. “Isis will never be able to take this city,” said Bahar, a resident speaking from the office of the defence minister, Ismet Hasan. “We are prepared to face them inside Kobani – if they enter, this city will become their grave.”

Bahar said the city was under heavy attack from all sides. “They fire missiles and rockets at the city, they use heavy weaponry to attack us here. But if they think they can take the city like this they are wrong; that’s a miscalculation.”

Bahar also said thousands of civilians were still in Kobani, contrary to some reports. “Many of these people don’t want to leave, but stay and defend their own land. Others came back from Turkey to fight.”

Many Kurds from Turkey have also joined the fight against Isis. According to the pro-Kurdish newspaper Özgür Gündem, at least 11 of 25 YPG fighters killed in the past 17 days had Turkish passports.

Idris Nassan, Kobani’s deputy foreign affairs minister, confirmed volunteers from Turkey had arrived in Kobani, but said many of them had little or no fighting experience. “Some have done their military service, but some have no experience at all,” said Nassan. “We need to train them first. The YPG does not take these volunteers to the frontlines, they help out with other means.”

Nassan also stressed there was no lack of fighters, but of weaponry and ammunition. “We need heavy weapons and more ammunition, we are running low, all we have is ammunition for light arms.”

Air strikes conducted by the US-led coalition have not slowed the Isis advance, and Nassan said strikes in Raqqa and Idlib had made matters worse. “Isis fighters from these provinces come to join the fight on Kobani; they run from there to come here. We need air strikes to help us.”

He urged the international community to step up both military and relief efforts to help Syrian Kurds. “We have no hospitals here anymore, and few medical supplies. We are running low on everything: food, water, milk for children.” Most of the supplies available were now coming via Turkey, he explained, often through Kurdish organisations. Injured people are being treated in Turkish hospitals.

Nassan warned that an Isis victory in Kobani would lead to atrocities: “Isis has been trying for a year to take Kobani and has always failed. They have suffered huge losses. If they manage to come here, they will rape and kill and slaughter.”

The Pentagon said the US-led coalition had conducted at least seven air sorties against Isis around Kobani in the five days to Wednesday, but there were no reports of any strikes on Thursday or Friday.

Catherine James in Suruc on the Turkish-Syrian border, and Constanze Letsch in Istanbul