Islamic State

Militants shell a beleaguered Syrian Kurdish town near the border with Turkey.

BEIRUT — Islamic State militants shelled a beleaguered Syrian Kurdish town near the border with Turkey on Sunday, sending smoke billowing into the sky as Kurdish militiamen scrambled to repel the extremists’ offensive, activists said.

The Islamic State group has pushed to the outskirts of the town of Kobani, also known as Ayn Arab, as it presses its weeks-long offensive against the city and its surrounding villages. The assault has forced 160,000 people to flee across the frontier in one of the biggest single exoduses of Syria’s civil war.

The Islamic State group has continued to advance despite air strikes against its fighters by the U.S. and its Arab allies. Overnight, coalition strikes targeted militant positions around Kobani, according to the Britain-based Syrian Observatory for Human Rights, an activist group.

The U.S. military said fighter aircraft conducted two strikes northwest of the city of Raqqa, hitting a large Islamic State group unit and destroying six militant firing positions. The statement did not specify the location, but Kobani is northwest of Raqqa.

The Observatory said that the strikes, combined with heavy clashes on the ground overnight, left at least 16 militants dead. At least 11 Kurdish militiamen were also killed in the fighting.

On Sunday, the extremists, who have staked out positions to the east, west and south of Kobani, shelled the town with rockets, mortars and tank shells, the Observatory said. There was also heavy fighting for control of a strategic hill south of the town.

From the Turkish side of the border, the heavy thud of the shelling could be heard, along with the sharp crackle of small arms fire, while pillars of smoke billowed from inside Kobani.

Some of the fighting has spilled over into Turkey, with artillery rounds falling on Turkish soil.

On Sunday, one shell fired from the Syrian side struck a house in the Turkish village of Buyuk Kendirci, wounding four people. A member of the family that owns the house, Dogan Polat, said that a 5-year-old child was among the injured.

Gov. Izzettin Kucuk said authorities were evacuating two villages close to the border.

The fighting between the Islamic State group and the Kurds is one aspect of Syria’s multilayered civil war, which has killed more than 190,000 people since the revolt against President Bashar Assad began in 2011.