Over the past two weeks, Iraqi forces have overrun several districts and, for the first time, reached the Tigris River that runs through the heart of the city.
In the eastern front, the elite forces of Iraq's Counter-Terrorism Service (CTS) recaptured the neighborhood of 7th Nisan and cleared the adjacent neighborhood of Sukkar, amid fierce clashes with the extremist militants, a statement by the Iraqi Joint Operations Command said.
Carter said the decision to keep a residual USA military presence in Iraq would be up to the Iraqi government and Prime Minister Haider al-Abadi.
While more than 200,000 have fled their homes to camps around the city since the offensive began in mid-October, tens of thousands more are thought to have stayed through the fighting and are living in dire conditions.
United Nations humanitarian spokesman Jens Laerke said almost 700 people had been taken to hospitals in Kurdish-controlled areas outside Mosul in the last week and more than 817 had required hospital treatment a week earlier.
The battles in Mosul came as the CTS commandos, army troops and federal police launched on December 29 the second phase of a major offensive to free Mosul.
According to Reuters, Isis militants have been resisting the advance of Iraqi forces with suicide auto bomb attacks and snipers and managed to slowdown them down in November and December by using tunnels that were close to civilian population.
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A top Iraqi commander, Lt. Gen. Talib Shaghati, told The Associated Press that the operation to retake Mosul from ISIS could be complete in three months or less. "The challenge is that they (IS) are hiding among civilian families, that's why our advances are slow and very cautious", Lieutenant-Colonel Abdel Amir al-Mohammedawi, a spokesperson for the rapid response units of Iraq's federal police, told Reuters.
He said rapid response units and Iraqi army units had fought their way into the Palestine and Sumer districts in the last day, but that IS fighters were firing at civilians trying to flee.
"Trauma casualties remain extremely high, particularly near frontline areas", OCHA said.
"Whenever they (IS) withdraw from a district, they shell it at random, and it's heavy shelling", he added.
Islamic State jihadists are using small commercial drones to attack Iraqi security forces in the battle for Mosul, a USA commander said Wednesday.
Mekko said: "Many families have not yet decided what they will do".