Brigadier General Matthew Isler, deputy commanding General of the US Air Force, said: “Right now, the offensive is going very well.”
He said that on Sunday, the Iraqi security forces had continued their advance into west Mosul, moving into a new neighbourhood to the west of Old Mosul and new areas in the north and the west of the city.
Speaking from Baghdad, he said: “We are today 35 days into west Mosul operations.
“The Iraqi security forces are making continuous progress and Daesh (Islamic State) is fighting very hard to resist but they are unable to deny the Iraqi security forces their objectives.
“So we are witnessing the defeat of Daesh.”
The battle is not easy, however, with Iraqi soldiers facing “a violent existence” and “tough fight for survival” against weapons such as cars hollowed out with home-made explosives, snipers, suicide bombers and machine guns, he said.
Islamic State has also taken over homes, schools, churches and mosques to defend the city, he added.
Brig Gen Isler’s words come amid concerns about civilian casualties, such as those during an airstrike in west Mosul last week which Iraqi officials say claimed more than 100 civilian lives.
US Central Command said in a statement that “an initial review of strike data from March 16-23 indicates that, at the request of the Iraqi Security Forces, the Coalition struck ISIS fighters and equipment, March 17, in West Mosul at the location corresponding to allegations of civilian casualties”.
It is impossible to independently confirm the number of dead, but Laith Habbaba, head of Nineveh’s health directorate, said 160 bodies had been found and buried after the single airstrike on 17 March.
An Iraqi brigadier general told AFP that at least 27 residential buildings had been badly damaged when the attack was called in to deal with a number of Islamic State snipers.
But Reuters quoted Iraq’s military as saying that 61 bodies had been recovered from a destroyed building booby-trapped by Islamic State, but that there had been no sign the building had been hit by a coalition airstrike.
General Joseph Votel, who heads the US Central Command, said on Sunday that the recent civilian deaths in Mosul were a “terrible tragedy” but he stopped short of taking responsibility.
Brig Gen Isler said the coalition was investigating what had happened, adding: “We will use the results of those investigations to make sure that our tactics, techniques and procedures take every feasible measure to protect civilians from harm.
“The coalition takes every allegation seriously and investigates all credible allegations.”
He added that Iraqi soldiers design their own operations to protect civilians and to gain a foothold in Mosul they had first secured an airport and military complex where there was no civilian activity.
Each strike is requested by an Iraqi officer and “often we make a decision to not even strike if the risk to innocent civilians is too high”, he said.
Nawfal Hammadi, the governor of Nineveh province, of which Mosul is the capital, has also accused IS of putting Mosul residents in harm’s way.
“The Daesh terrorist organisation is seeking to stop the advance of the Iraqi forces in Mosul at any cost, and it is gathering civilians… and using them as human shields,” he said.
The United Nations has called for all sides to protect civilians during the battle.
:: Watch a special programme, The Battle For Mosul, at 12pm and 7pm on Monday on Sky News.