MURSITPINAR, Turkey — Gun battles and explosions echoed from the embattled Syrian Kurdish town of Kobani on Wednesday, as Islamic State militants detonated a car bomb and new American-led airstrikes hit the northern edge of the town, close to the Turkish border.

A Kurdish official in Kobani, Asia Abdullah, said that despite the bombing, Islamic State fighters had managed to enter new areas of the town and move north, closer to the border.

That development, along with what could be seen of the fighting from across the border, suggested that two days of intensive airstrikes had failed to turn back the militants. Kurdish fighters, as well as Turkey’s president, Recep Tayyip Erdogan, have said that airstrikes alone will not stop the attackers.

But they are divided on how to address the problem. Kurds insist that Turkey should allow Kurdish fighters, supplies and weapons to enter the encircled town through its territory. Turkey refuses to do so unless the Kurds meet certain demands, including distancing themselves from their allies in an outlawed Kurdish separatist party in Turkey.