Iraqi army's chief of staff, Lieutenant General Othman al-Ghanmi, says the battle against Daesh for the city of Mosul will finish "in a maximum of three weeks."
A top Iraqi commander expects to dislodge Daesh from Mosul in May despite resistance from militants in the densely populated Old City district.
The battle should be completed "in a maximum of three weeks," the Iraqi army's chief of staff, Lieutenant General Othman al-Ghanmi, was quoted as saying by state-run newspaper al-Sabah on Sunday.
A US-led international coalition is providing air and ground support for the offensive in Mosul, the largest city in northern Iraq.
Daesh has lost most of the city's districts since the offensive began in October and is now surrounded in the northwestern districts, including the historic Old City centre.
The United Nations believes that up to half a million people remain in the area still controlled by the militants in Mosul, 400,000 of which are in the Old City with little food and water and no access to hospitals.
The militants have dug in between the civilians, often launching deadly counter-attacks to repel forces closing in on the Old City's Grand al-Nuri Mosque.
It was from this mosque, famous for its leaning minaret, that the group's leader, Abu Bakr al-Baghdadi, had declared a caliphate over parts of Iraq and Syria. Mosul was by far the largest city to have fallen under his control in both countries.
Federal Police brigade commander killed
A Federal Police brigade commander and 18 other members of the interior ministry force were killed in attacks on two positions at the edge of the Old City on Friday, military sources said on Sunday.
Federal Police took back the two positions on Saturday but the interior ministry has sacked a top commander for failing to fend off the counter-attacks, the sources said.
The US-trained Counter Terrorism Service and Federal Police are the main forces fighting inside Mosul. Regular Iraqi army units are taking part in battles outside the city, alongside Shi'ite volunteers trained and armed by Iran, Kurdish Peshmerga fighters and Sunni tribes.
The total number of fighters aligned against Daesh in Mosul from all forces and units exceeds 100,000.
Iraqi forces estimate the number of Daesh militants who remain in Mosul at 200 to 300, mostly foreigners, down from nearly 6,000 when the offensive started.
Several thousand have been killed so far in the battle, both civilians and military, according to international aid organisations. The total number of people displaced from Mosul since October is close to 400,000, about a fifth of Mosul's population before its capture by Daesh.