According to the IOM, more than 238,000 people are now displaced due to fighting in the Mosul area, while more fled but later returned to their homes.
Iraqi security forces said at the weekend they had entered the Bab al Tob area of the Old City, where fighting is expected to be toughest because of its narrow alleyways, where armoured vehicles can not pass. The operation to retake Mosul was launched in October more than two years after the extremists took control of Iraq's second largest city.
The forces launched a major push last month to oust the IS militants from west Mosul, taking back a series of neighbourhoods as well as sites including the city's airport, the Mosul museum and the provincial government headquarters.
The total number of Iraqis to have been displaced from western Mosul now stands at 111,000, according to Iraqi Minister of Displacement and Migration Jassim al-Jaff, who added that the ongoing displacement rate had reached between 7,000 and 8,000 people per day.
CTS and the interior ministry's Rapid Response Division - a special forces unit operating with members of the federal police - are spearheading the advance in west Mosul.
Losing the city would be a huge blow to Islamic State as it has served as the group's de facto capital since its leader Abu Bakr al-Baghdadi proclaimed himself head of a caliphate spanning Iraq and Syria from the Nuri Mosque in July 2014. "Any of the fighters left in Mosul, they're going to die there", McGurk said in a conference in Baghdad.
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An air strike targeting one Islamic State position hit a building, engulfing nearby troops in smoke and dust.
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.
Iraqi forces took full control of eastern Mosul at the end of January, 100 days after the US-backed campaign to dislodge Daesh militants from the city began. Tens of thousands have been pouring into camps outside Mosul.
Ashraf Ali, a nurse who escaped with his wife and two children, said mortar rounds were falling as they fled. "If there are civilians, families in the homes, we shout to them to take cover inside a room", the soldier lamented.
"Daesh is a common foe that we need to face", Mr Hishammuddin told reporters, using an Arab acronym for ISIS, after meeting Australian Foreign Minister Julie Bishop in parliament. "There are more people on this side of the city and people are trying to leave because there is no food and no supplies in their area".