US-backed forces trying to oust Islamic State militants from the Syrian city of Manbij took "almost complete control" of the city on Saturday, the Syrian Observatory for Human Rights said.

The Syria Democratic Forces, which includes the powerful Kurdish YPG militia and Arab fighters, launched its campaign two months ago with the backing of US special forces to drive Islamic State from a last stretch of the Syrian-Turkish frontier.

Pockets of Islamic State militants are still present in the center of the city, the Britain-based Observatory said.