In addition, he said that IS forces since Saturday night had suffered "heavy casualties in their ranks and losses of vehicles and weapons" in those bombardments.
Sinjar is located some 120 km west of Mosul, the capital of Nineveh province, which has been under IS control since last June.
More than 400,000 members of the Yazidi ethnic group - a Kurdish religious minority - fled the area last August to take refuge in the neighbouring autonomous region of Iraqi Kurdistan as IS forces moved into the area, committing atrocities against the local population.
The US military began bombing IS positions in Iraq Aug 8 and since then Washington has been trying to build an international coalition to reinforce this campaign.
Last Friday, French military air units joined the operations in Iraq conducting their first bombardment of IS positions.