BEIRUT (REUTERS) - Islamic State fighters have seized more than a third of the Syrian border town of Kobane despite US-led air strikes targeting them in and around the town, a monitoring group said on Thursday.

They moved into two districts on Wednesday in a three-week battle that Kurdish defenders say will end in a massacre and give the militants a garrison on the Turkish border if they win.

The commander of Kobane's heavily outgunned Kurdish defenders said Islamic State controlled a slightly smaller area. However, he acknowledged that the militants had made major gains in the culmination of a three-week battle that has also led to the worst streets clashes in years between police and Kurdish protesters across the frontier in southeast Turkey.

Esmat al-Sheikh, head of the Kurdish militia forces in Kobane, said Islamic State fighters had seized about a quarter of the town in the east: "The clashes are ongoing - street battles."

The Syrian Observatory for Human Rights, which monitors the country's civil war, said clashes continued in the morning as the forces of Islamic State - still widely known by its former acronym of ISIS - pushed forward.

"ISIS control more than a third of Kobane. All eastern areas, a small part of the northeast and an area in the southeast," the Observatory's head, Rami Abdulrahman, said by telephone.

An explosion was heard on Thursday on the western side of the mainly Kurdish town, with thick black smoke visible from the Turkish border a few kilometres (miles) away. The sound of a jet flying overhead and sporadic gunfire from the besieged town was audible. Several ambulances sped from the border to the town of Suruc in Turkey.

Islamic State hoisted its black flag on the eastern edge of Kobane on Monday. Since then, the air strikes have been redoubled but failed to halt the advance.

In Washington, the Pentagon cautioned that there are limits to what the air strikes can do in Syria before Western-backed, moderate Syrian opposition forces are strong enough to repel Islamic State. US President Barack Obama has ruled out sending American ground forces on a combat mission there.

Kurds have complained that Washington is giving only token support through its air strikes, which are focused in Iraq where the United States works with the Iraqi Army.

Secretary of State John Kerry said on Wednesday: "As horrific as it is to watch in real time what is happening in Kobane ... you have to step back and understand the strategic objective."