(Reuters) - Kurdish ground forces, helped by U.S. and allied air support, have retaken the Syrian town of Kobani from Islamic State militants, U.S. Lieutenant-General James Terry said on Saturday.

Supporting what Kurdish forces said earlier this week, Terry, commander of the Combined Joint Task Force that has been leading air strikes against Islamic State, said in a statement issued by the U.S. military: "Kurdish ground forces, supported by our air component, were successful in retaking the town of Kobani."

A monitoring group and Syrian state media reported Kurdish fighters took full control of Kobani on Monday, but on Tuesday a U.S. official said the town on the Turkish border had not been fully retaken.

Saturday's statement said Kurdish forces had pushed Islamic State out of Kobani on Tuesday.

"Kurdish forces continue to expand their positions to surrounding areas outside of Kobani by seizing key terrain and access routes," it said.

The United States and allies have launched more than 700 air strikes against Islamic State in and around Kobani since Aug. 8, destroying more than 280 fighting positions, nearly 100 buildings, more than 60 technical vehicles and other equipment, it said.

Islamic State, which has seized parts of Syria and Iraq, launched an assault on the predominantly Kurdish town last year, using heavy weapons seized in Iraq and forcing tens of thousands of residents into exile.

(Reporting by Mohammad Zargham; Editing by Frances Kerry)