Isis fighters have pushed to the edge of Kobani and evade western strikes, says spokesman for Kurdish fighters

US-led air strikes in northern Syria have failed to interrupt the advance of Islamic State (Isis) fighters closing in on a key city on the Turkish border, raising questions about the western strategy for defeating the jihadi movement.

Almost two weeks after the Pentagon extended its aerial campaign from Iraq to neighbouring Syria in an attempt to take on Isis militants in their desert strongholds, Kurdish fighters said the bombing campaign was having little impact in driving them back.

Isis units have edged to within two kilometres of the centre of Kobani, according to Kurds fighting a rearguard action inside the city. The jihadis, who this weekend generated further outrage with the murder of the British hostage Alan Henning, are simply too numerous to be cowed by the air assault by US fighter jets, the Kurds say.

“Air strikes alone are really not enough to defeat Isis in Kobani,” said Idris Nassan, a senior spokesman for the Kurdish fighters desperately trying to defend the important strategic redoubt from the advancing militants. “They are besieging the city on three sides, and fighter jets simply cannot hit each and every Isis fighter on the ground.”

He said Isis had adapted its tactics to military strikes from the air. “Each time a jet approaches, they leave their open positions, they scatter and hide. What we really need is ground support. We need heavy weapons and ammunition in order to fend them off and defeat them.”

The Britain-based Syrian Observatory for Human Rights has reported that warplanes have carried out repeated strikes in recent nights around Kobani. The Pentagon has reported daily on its aerial missions over Iraq and Syria since first deciding to go after Isis two months ago. But it does not pinpoint exact locations. “Two strikes north-west of Raqqa struck a large (Isis) unit and destroyed six firing positions,” it said on Sunday in a statement. Kobani is north-west of Raqqa.

But the claim that the aerial bombardment is not sufficient to turn the tide on the ground will unsettle those in the US-led coalition, including the UK government, who have signed up to an air war as the best way of taking the fight to Isis.

In Washington, military hawks continue to argue for an escalation of the war in Syria and Iraq with the deployment of US ground troops – a move that Barack Obama has repeatedly ruled out.

“The strategy of aerial bombardment is not going to work to destroy Isil [Isis],” the South Carolina senator Lindsey Graham told CNN. “You cannot destroy Isil without a ground component.” He argued that training the inexperienced fighters of the Free Syrian Army in Saudi Arabia was “militarily unsound” and “will lead to their slaughter”.

His words were echoed in London by the former chief of the defence staff General Sir David Richards. “Air power alone will not win a campaign like this,” he told BBC1’s Andrew Marr Show. “It isn’t actually a counter-terrorist operation. This is a conventional enemy in that it has armour, tanks, artillery … it is quite wealthy, it holds ground and it is going to fight. So therefore you have to view it as a conventional military campaign.”

Nick Clegg, the deputy prime minister, disagreed. “How you respond is not quite as straightforward as David Richards, much as I respect him, suggests,” he said. “I don’t think it is a question of simply ramping up conventional armed forces again as if we were fighting state-to-state conflicts.”

Clegg said states would cooperate in a “jigsaw” operation in which different countries bring different capabilities against “stateless mobile troops”. But Britain has thus far committed only to air strikes over Iraq, and Clegg said he was opposed to stepping up the British action. “I wouldn’t advocate extending the air campaign into Syria which is why we didn’t do it last week,” he said. The prime minister,

David Cameron, will not propose a vote on Syrian air strikes unless the Lib Dems and Labour agree.

But appetite to confront Isis remains undiminished in the light of the grim succession of the murders of hostages. Cameron vowed at the weekend to use “all the assets we have” to secure justice for Henning, whose murder was broadcast online on Friday night, making him the fourth captive to be killed in six weeks. Isis has threatened to kill an American aid worker, Peter Kassig, next.

Kobani has emerged as the most important flashpoint between Kurds and jihadists in Syria because of the strategic importance of the city and the sheer numbers of Kurds who sought refuge there in recent months. More than 160,000 have fled to Turkey in the face of the Isis advance, sharply aggravating historic tensions between Turks and Kurds. On Sunday, a stray shell hit a village on the Turkish side of the border, injuring five people.

MPs and representatives of Kurdish groups in Turkey arrived at the border to show solidarity with Syrian Kurds and to form a “human chain” stretching along villages bordering Kobani. Meanwhile, Saleh Muslim, co-chair of the Syrian Kurdish Democratic Union party (PYD), went to Ankara this weekend to hold meetings with Turkish security officials to discuss possible Turkish assistance in defending Kobani against Isis. Turkey’s government has vowed it will not sit idly by and let Kobani fall.

Turkish media reported that security officials in Ankara urged Muslim to convince the YPG, the armed wing of the PYD that is currently battling Isis in Kobani, to join the ranks of the Free Syrian Army (FSA) and to “take an open stance against the Syrian regime” of Bashar al-Assad.

“We are calling on the international community to help us defend Kobani,” said Nassan.

He said the exact outcome of the meetings remained unclear, but hinted that Muslim had asked Ankara to allow for the PYD, the Syrian Kurdish affiliate of the better-known Kurdistan Workers’ party (PKK), to receive arms from outside of Syria.

“If Isis takes Kobani, they will be right on the border with Turkey. This concerns not only us, but Turkey, too.”