The Iraqi troops have managed to retake 352 square km from the southern parts of Mosul from the foreign-backed terrorists, the Arabic-language al-Ahed news website reported on Wednesday.
The Iraqi army launched the offensive on Sunday aimed at wresting Mosul from the hands of Daesh.
"The time has come for the greatest victory," Iraqi Prime Minister Haider al-Abadi announced late Sunday on state TV. "I announce the start of Liberating Mosul Operation, by the will of Iraqis, and after depending on Allah."
Al-Abadi said that Daesh would be "punished" for its crimes and that the province's cities and villages will be rebuilt.
"We will rebuild what those criminals have destroyed," he said. "We will bring life back to Mosul and all other areas around Mosul."
In a statement, US Secretary of Defense Ash Carter called the offensive a "decisive moment in the campaign to deliver (Daesh) a lasting defeat."
Though the operation began Sunday, its plans had been known long before.
Iraq's air force dropped leaflets warning Mosul residents that the liberators are coming, and the Baghdad government directed broadcasts directly into the heart of the occupied city.
Meanwhile, Iraqi forces have circled the country's second-largest city and cut off any supply — or escape — routes that the Daesh fighters holed-up in Mosul could use.