The British-based Observatory said the Kurdish YPG militia made up the majority of forces involved in the attack, contradicting U.S. officials who said the operation would be mostly comprised of Syrian Arab fighters.
Turkey is opposed to any further expansion of Syrian Kurdish influence in northern Syria, where the YPG already controls an uninterrupted 400 km (250 miles) stretch of the border.
U.S.-led air strikes killed 15 civilians including three children near Manbij in the last 24 hours, the Observatory said.
"The majority are from (YPG), and the operation is basically a YPG operation," Abdulrahman told Reuters.
U.S. officials told Reuters thousands of fighters, supported by a small number of U.S. special forces, were launching an offensive to capture the crucial swathe of northern Syria that militants have long used as a logistics base.
The Observatory said the assault was being carried out by the Syria Democratic Forces, an alliance that includes the Kurdish YPG and Arab fighting groups.
Washington supports the SDF, which was formed in October, has been fighting Islamic State in neighbouring Raqqa province and farther east in Hasaka.
The YPG has been the most effective ally on the ground for U.S.-led air strikes against IS, and last year captured large areas from it in Hasaka province.