The overthrow of President Bashar al-Assad by Isis and rebel groups that are affiliated to al-Qaeda would be a calamity for the world, says the Syrian Kurdish leader Saleh Muslim.

In an interview with The Independent he warned that “if the regime collapses because of the salafis [fundamentalist Islamic militants] it would be a disaster for everyone.”

Mr Muslim said he was fully in favour of Mr Assad and his government being replaced by a more acceptable alternative. But he is concerned that Isis and other extreme Islamist groups are now close to Damascus on several sides, saying that “this is dangerous”. During a recent Isis offensive in the north eastern city of Hasaka, the Kurdish YPG (People’s Protection Units) militia and the Syrian Army both came under attack from Isis, but Mr Muslim denied that there was any collaboration between the two.

The Syrian Kurds, previously marginalised and discriminated against by the Damascus government, have become crucial players in the country’s civil war over the last year. In January, they defeated Isis at Kobani with the aid of US airstrikes after a four-and-a-half month siege and their forces are still advancing. While Mr Muslim said that he wants an end to rule by Mr Assad, he makes clear that he considers Isis to be the main enemy.

“Our main goal is the defeat of Daesh [Isis],” he said. “We would not feel safe in our home so long as there is one Daesh [Isis] left alive.” The threat did not come from them alone, he said, but also from al-Qaeda clones such as Jabhat al-Nusra and Ahrar al-Sham. “They all have the same mentality.”

Mr Muslim is the president of the Democratic Union Party (PYD) that rules Rojava, as Kurds call the three Kurdish enclaves just south of the Turkish border. A stocky and affable man, aged 64, he apologised before the interview in the city of Ramalan for his broken English – though it turned out to be fluent, something explained by a year spent in Britain learning English and 12 years as an oil industry engineer in Saudi Arabia, where the working language was also English.

Saleh Muslim, president of the PYD , feels Isis is a bigger threat, compared to the Syrian army (AFP/Getty)

He says he is still surprised by the speed with which the Syrian Kurds have emerged from obscurity, since the withdrawal of the Syrian army from Kurdish enclaves in 2012, to become a major force in Syria. The highly-disciplined and committed YPG fighters have won victories over Isis this year at Kobani, Tal Abyad and Hasaka, at the same time that Isis was inflicting defeats on both the Iraqi and Syrian armies.

Mr Muslim and other PYD leaders now face an important decision about the future advance of YPG forces. Having retaken Kobani and 380 villages nearby, they are currently dug in on the east bank of the Euphrates River, close to Isis’s last remaining border crossing to Turkey at Jarabulus and to a larger, strategically important, area north of Aleppo. Turkey is wary of the YPG and is eager to create a so-called “safe zone” which would be held by Syrian opposition groups under its influence – ostensibly to keep Isis from its borders but thus also preventing Kurdish forces from advancing westwards.

Mr Muslim says the present situation cannot continue in this area because Kurdish civilians there are being attacked by Isis. Only the previous day, he said, 300 Kurds had been forced out of their homes in the Isis-held town of Manbij, where Kurds make up 30 per cent of the population, and seven people had been killed. Another 150 Kurdish villages are under threat.

Mr Muslim stressed the YPG was acting to defend not only Kurds, but all Syrians under attack by Isis. He said that if people living in the zone west of the Euphrates and north of Aleppo were “to ask the YPG for help” they would most likely get it. In addition, the Kurds want to open a road to a third Kurdish enclave at Afrin, which is isolated and under threat.

Noting the US wants an Isis-free zone in this area, Mr Muslim said “the perfect way to do this is ground troops and air support”. It is not entirely clear that the US will go along with this and give the YPG the air cover it may need, because it does not want to offend Turkey. However, the Syrian armed opposition is almost wholly dominated by Isis and its al-Qaeda equivalents, so the US does not want to damage the successful collaboration between YPG ground troops and US air power.

How would Turkey respond to a further Kurdish advance? It is already alarmed by the rise of a Kurdish state-let in the form of Rojava on its southern frontier with Syria. It knows that the PYD is essentially the Syrian branch of the Kurdistan Workers’ Party (PKK) against whom it has been fighting a guerrilla war since 1984. Mr Muslim said: “I do not think it is possible that Turkey will invade, but if it does it will be a big problem for Turkey.”

Though the YPG is America’s most effective military ally against Isis in both Iraq and Syria, Washington remains ambivalent about the extent of its co-operation with the Syrian Kurds. Mr Muslim says that “the Americans have not delivered any weapons or ammunition to the YPG”.

They have reassured him their support for the Syrian Kurds will not be weakened by their agreement with Turkey, signed in July, for the US to use Incirlik airbase and for Turkey to join attacks against Isis.

In the event, Turkey launched few air raids against Isis and many hundreds against the PKK in south-east Turkey and northern Iraq. Mr Muslim says that since detachments of the PKK in northern Iraq are fighting Isis, the Turkish actions can only benefit the Islamic militants. He is only partially comforted by American reassurances, saying what worries him is “what has not been revealed” about the US-Turkish deal.

In the course of the interview, Mr Muslim would periodically say that the situation was confusing, but he is adept at seeking to conciliate rival powers. He had just returned from a meeting with President Masoud Barzani, who heads the Kurdistan Regional Government in northern Iraq and is himself wary of the sudden appearance of a rival Kurdish quasi-state in northern Syria. The KRG has been enforcing an intermittent embargo against Rojava, with some trucks waiting a couple of months on the frontier. Mr Muslim said the border was opening and closing “according to the mood” of KRG authorities.

He is dubious about reports of Russian troops joining the war in Syria. He had been in Moscow last month and had been assured that the Russians “would not do that. [Russian special envoy for Syria Mikhail] Bogdanov said to me that they would not be involved in the fighting.”

Though he is determined to fight Isis until it is defeated, Mr Muslim believes that the Syrian civil war must end in a compromise.