Syrian rebels advanced into an Islamic State-held town at the border with Iraq on Wednesday”, a rebel commander told reporters, in a new U.S.-backed offensive aimed at splitting the jihadists’ self-declared caliphate in two.

The operation aiming to capture the eastern Syrian town of Al-Bukamal, which began on Tuesday, adds to the pressure facing Islamic State as it faces a separate, U.S.-backed offensive in northern Syria aimed at driving it away from the Turkish border.

The offensive is being waged by rebels of the new Syria Army formed some 18 months ago from insurgents driven from eastern Syria at the height of Islamic State’s rapid expansion in 2014.

Rebel sources say it has been trained with U.S. support.

The clashes are inside the (town) and matters are not yet settled,” said the rebel commander of the Asala wa-al-Tanmiya Front, one of the main elements of the New Syria Army, “the rebel forces entered the town at dawn”, he said.

The Syrian Observatory for Human Rights said the offensive was being mounted with backing of Western special forces and U.S.-led air strikes.

Islamic State’s capture of Al-Bukamal in 2014 effectively erased the border between Syria and Iraq. Losing it would be a huge symbolic and strategic blow to the cross-border “caliphate” led by Abu Bakr al-Baghdadi.