A Kurdish militia leading an attack on Islamic State strongholds in Syria so far has no plan to extend the assault to the group's de facto capital of Raqqa city, and such an advance should be led by Syrian rebels, a Kurdish leader said on Wednesday. The comments by Saleh Moslem, leader of the Democratic Union Party (PYD), indicated there is no imminent offensive on Raqqa city by the Kurdish-led forces that have made swift gains against the jihadists backed by U.S.-led air strikes. Backed by smaller Syrian rebel groups, the Kurdish YPG militia moved to within 50 km (30 miles) of Raqqa city on Tuesday with the capture of the town of Ain Issa in northern Syria, backed by U.S.-led air strikes. Driven from areas north of Raqqa, Islamic State was reported to be reinforcing its positions near the city on Wednesday, digging trenches and bringing in truck loads of weapons. But Moslem, whose party holds sway in Syria's Kurdish areas, said it was up to rebel groups fighting with the YPG to decide on any advance on Raqqa itself. "We spoke to the YPG leadership. They don't have a plan toward Raqqa so far. This (decision) is linked to the revolutionary forces in Raqqa," Moslem said in a telephone interview. "When they are ready to free Raqqa, to liberate it, perhaps the YPG will decide to support them. But the YPG have not made a decision in this regard so far," he said. The YPG has emerged as the only notable partner on the ground to date for the U.S.-led alliance bombing Islamic State in Syria, and has fought several successful campaigns against the jihadists with air support. Moslem's comments indicate the well-organized YPG's reluctance to venture far beyond Kurdish areas to attack Islamic State in parts of Syria where Arabs are in the majority: the YPG's stated aim is to defend the Kurdish areas.