US-backed Iraqi forces are set to reach the main government complex in Mosul, their next target in the battle to retake the city from Islamic State.
The site should be taken on Monday, Lieutenant Colonel Abdel Amir al-Mohammadawi told the Reuters news agency.
Meanwhile, Colonel John L Dorrian, spokesman for Operation Inherent Resolve, the American-led coalition against IS, told Sky News the Iraqi forces were "imposing their will on the enemy" in the city.
"They're not going to be pushed out of Mosul - they're going to surrender or they're going to be killed there," he vowed.
A senior commander said earlier Iraqi troops had been involved in the "heaviest" clashes yet with IS fighters in the west of the city since the start of their offensive.
Major General Haider al-Maturi of the Federal Police Commandos Division told the Associated Press the militants had dispatched at least six suicide car bombs, which were all destroyed before reaching Iraqi forces.
He said IS fighters are moving from house to house and deploying snipers.
Iraqi forces launched attacks against IS-held neighbourhoods in western Mosul from three points on Sunday morning.
IS fighters have "some mortar (teams) and snipers positioned inside homes," Iraqi special forces Major Ali Talib said, adding that US-led coalition airstrikes have helped destroy some IS defences, but clashes were continuing.
As the fighting continues, the total number of civilians displaced from the city has risen over the last few days.
More than 200,000 civilians have been forced to flee their homes, according to the International Organisation for Migration.
International aid agencies have voiced fears that camps to accommodate displaced people are approaching full capacity.
The push to recapture the west of the city was launched around two weeks ago after the eastern half of Mosul was declared "fully liberated" in January.
The overall operation to retake the city - which IS has held since the summer of 2014 - began in October after more than two years of slowly taking back territory from IS militants.