U.S.-led coalition strikes supporting Iraqi forces in the recapture of Falluja have killed 70 Islamic State militants including the group's commander in the city, a U.S military spokesman said on Friday.

Iraqi government forces make gains in their offensive to drive Islamic State militants from Falluja - one the country's two major cities in IS hands.

Iraqi forces recaptured the last district held by Islamic State militants in the city of Falluja on Sunday and the general commanding the operation declared the battle complete after nearly five weeks of fighting.