But spokesman Peter Cook warned that the campaign "could take some time" to as it remained to be seen whether the jihadist group would "stand and fight".
Fighting continued overnight, with IS militants attacking Iraqi army tanks.
A BBC correspondent with an army unit says the southern frontline is still some 40km (24 miles) from the city.
IS militants overran Mosul in June 2014, before taking control of much of northern and western Iraq.
Their leader, Abu Bakr al-Baghdadi, chose a mosque in the city as the place to proclaim the establishment of a "caliphate", so retaking the city would be "symbolic", according to Mr Cook.