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Iraqi forces continued their advance into the ISIS-held western area of the country’s second-largest city on Tuesday, closing in on Mosul's strategic airport.

Troops continued clearing the hills around Abu Saif and successfully cleared two villages southwest of Mosul, according to a statement from the Iraqi military.

The action comes after soldiers engaged in heavy fighting with ISIS militants in the area on Monday, as they sought to take control of a hill overlooking the airport. Helicopters pounded the militants’ positions with rockets.

The Iraqi military aims to take control of the airport itself, to use it as a close support base as the offensive moves beyond the outskirts of Mosul.

However, a senior Iraqi security force told NBC News that the country's forces were planning a slow advance in their operation to retake all of Mosul, in order to minimize losses.

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Speaking on condition of anonymity because he wasn't authorized to speak to the media, the source added that the operation to drive ISIS out of the western part of Mosul would likely last until late May or early June.

"It’s a pretty impossible decision either way"

The operation involves Iraqi army troops and militarized police, backed by air power provided by a U.S.-led coalition.

U.S. special operations troops are also embedded with some Iraqi units and thousands of U.S. troops are in the country providing logistical and other support.

The offensive is part of a wider campaign which began in November, that has already driven ISIS fighters from the eastern half of the city. ISIS seized Mosul in 2014 and it is now the last urban center in Iraq controlled by the group.

As the operation began Sunday, Iraqi forces dropped leaflets over the city urging ISIS fighters to surrender.

The risk of civilian casualties as the operation progresses into the heart of Mosul will increase significantly. There are 750,000 civilians in the western section of the city, according to the United Nations.

Iraqi rapid response forces are seen through a shattered glass window of a military vehicle south of Mosul on Monday. Alaa Al-Marjani / Reuters

Those civilians are facing an increasingly dire humanitarian situation, with only 40 percent of those trapped in the western part of the city having access to clean drinking water and 80 percent of basic items not available to most people, according to Georgina Sword Daniels, an advocacy adviser with the International Rescue Committee.

In addition, those trapped in the city face a dilemma as the Iraqi military approaches: to stay and risk being becoming a casualty of the conflict, or to try and flee, but risk ISIS' wrath.

"If they decide to stay they might get caught in the crossfire," Daniels told NBC News. "If they flee, they face a very dangerous journey, going across front lines, maybe being shot at by ISIS."

She added: "Also, there are a lot of landmines and explosive devices lying around the city. We’ve seen from other places in Iraq that have previously been held by ISIS, people have come across these devices and been killed and injured by them. It’s a pretty impossible decision either way."