Since starting the offensive Iraqi forces have retaken eastern Mosul and about 30% of the west of the city.
Troops were also concentrating on capturing the Iron Bridge linking eastern Mosul with the Old City on the western side of the Tigris river, where Islamic State fighters are preparing to make a last stand.
Near the Mosul Museum, Iraq forces used armored vehicles and tanks to attack snipers pinning down troops clearing areas around the bridge.
While the civilian death toll is impossible to calculate amid the ongoing battle for Iraq's second largest city, Sheikh Khamis Khanjar, the founder of the Office of the Sunni Arab Representative for Iraq, said at least 3,500 civilians have been killed in the battle for Mosul.
Neither the Iraqi government nor the USA coalition have announced civilian casualties in the biggest ground operation in Iraq since the U.S led invasion of 2003.
"Our forces are advancing toward their targets".
In addition to helping Iraqi forces retake territory, McGurk said the USA -led coalition has killed 180 ISIS leaders since the campaign against the militants began more than two years ago.
Earlier, Iraqi Prime Minister Haider Al Abadi said in Baghdad the battle to drive Islamic State (IS) militants from their last urban stronghold is in final stage.
"Speaking at a news conference on Tuesday night, he warned the insurgents that they must surrender or be killed although he also pledged to treat the militants' families fairly".
Ashraf Ali, a nurse who escaped with his wife and two children, said mortar rounds were falling as they fled.
However, they will likely make slow headway in the streets and narrow alleyways of the Old City as IS has booby-trapped houses, and government forces will also be fighting amongst civilians, ruling out extensive use of air and artillery support.
In November, State Department spokesman Mark Toner said that the USA takes "every effort" and "every precaution to avoid civilian casualties" across Iraq event to the point where the U.S. will call off a strike "against known enemy targets because they put civilians at risk".
As fighting intensified on Tuesday after the previous day's heavy rains, civilians streamed out of western neighborhoods recaptured by the government, cold and hungry but relieved to be free of the militants' grip.
In a related development, four Iraqi rapid-response personnel (affiliated with the Interior Ministry) were killed Monday evening when Daesh militants shelled their positions in central Mosul's Bab al-Toub district, Ahmed al-Jubouri, a colonel in the army's Nineveh Operations Command, told Anadolu Agency. IOM said the fighting in the Mosul area has displaced almost 240,000 people.
As many as 600,000 civilians are caught with the militants inside Mosul, which Iraqi forces have effectively sealed off from the remaining territory that Daesh controls in Iraq and Syria.
"Yesterday resistance was very strong in that area". Food had been scarce, they said.
Aerial surveillance photos showed women carrying guns. They had found 40 more such missiles stored in homes in Dor al-Sikak.
Mosul's fall would deal a significant blow to IS.