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BAGHDAD (Reuters) - Iraqi forces on Tuesday reported progress in the U.S.-backed campaign to dislodge Islamic State from Mosul, announcing the capture of a district just north the city’s historic center.

With the loss of the Zanjili neighborhood, the enclave still held by Islamic State in the northern Iraqi city has shrunk to two districts along the western banks of the Tigris river - the densely populated Old City center and the Medical City.

Iraqi government forces retook eastern Mosul in January and began a new push on May 27 to capture the remaining enclave, where up to 200,000 people are trapped.

The Mosul offensive started in October with air and ground support from a U.S.-led international coalition. It has taken much longer than expected as Islamic State is fighting in the middle of civilians, slowing the advance of the assailants.

The fall of Mosul would, in effect, mark the end of the Iraqi half of the “caliphate” declared in 2014 over parts of Iraq and Syria by Islamic State leader Abu Bakr al-Baghdadi, in a speech from a historic mosque in the old city.

In Syria, Kurdish forces backed by U.S.-air strikes are besieging Islamic State forces in the city of Raqqa, the militants’ de facto capital in that country.

About 800,000 people, more than a third of the pre-war population of Mosul, have already fled, seeking refuge either with friends and relatives or in camps.