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BAGHDAD — More than 40,000 people have been displaced in the last week from the Iraqi city of Mosul, where U.S.-backed forces launched a fresh push toward the ISIS-held old city center on Sunday and closed in on the main government complex.

The pace of displacement has accelerated in recent days as fighting approaches the most densely populated parts of western Mosul. Aid agencies have expressed concern that camps to accommodate people fleeing the city are almost full.

Iraqi police during a military operation Sunday at the western part of Mosul, Iraq. Omar Alhayali / EPA

The International Organization for Migration's Mosul Displacement Tracking Matrix showed that the number of people uprooted since the start of the offensive in October topped 206,000 on Sunday, up from 164,000 on Feb. 26.

That number may still rise sharply. The United Nations last month warned that more than 400,00 people, more than half the remaining population in western Mosul, could be displaced.

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Iraqi forces captured the eastern side of Mosul in January after 100 days of fighting, and they launched their attack on the districts that lie west of the Tigris River on Feb. 19.

Defeating ISIS in Mosul would crush the Iraqi wing of the caliphate that the group's leader, Abu Bakr al-Baghdadi, declared in 2014 over parts of Iraq and Syria.

Photos: Iraqis Stream Out of Mosul as Battle Against ISIS Intensifies

Rapid response units and counterterrorism forces launched a new push into the city on Sunday after a 48-hour pause caused by bad weather that hampered air surveillance, facilitating counterattacks by the militants.

Iraqi security forces transport civilians fleeing their homes during clashes between Iraqi security forces and ISIS on the western side of Mosul, Iraq, on Sunday. Khalid Mohammed / AP

Rapid response teams are "very close" to the government buildings near the old city, said a senior media officer with the elite Interior Ministry units. Their progress was met with heavy sniper and mortar fire, a Reuters photographer reported from Mosul.

The complex, which houses the Nineveh Provincial Council and the Nineveh Governorate buildings, should be taken on Monday, Lt. Col. Abdel Amir al-Mohammadawi told Reuters.

Recapturing the site would help Iraqi forces attack the militants in the nearby old city. It would also mark a symbolic step toward restoring state authority over Mosul, even though the buildings are destroyed and are not being used by ISIS.

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The Iraqi military believes several thousand militants, including many who traveled from Western countries, are hunkered down among the remaining civilian population, which aid agencies estimated to number 750,000 in western Mosul at the start of the latest offensive.

Several thousand people have been killed or wounded so far in the Mosul offensive, both civilians and military, according to aid organizations.