Trying to discern the Islamic State’s plans for defending the city, Staff Gen. Wathiq al-Hamdani, the commander of the Mosul police force, said that in recent days he had sent an informant, who was pretending to be a fisherman, to check under bridges for explosives. He said that the two bridges the informant was able to check — the city has five — were not rigged to blow up.

As the fight moves into the city, it will become simpler in one respect: Under the battle plan, only the Iraqi Army and the special forces are to enter the city proper. Other forces that have participated in the approach — the Kurdish pesh merga fighting to the north, and Shiite militias in the west — are being kept away because their presence would probably alienate Mosul’s Sunnis.

The fight for Mosul has played out against the backdrop of political uncertainty, with great unease about the potential for the battle to unleash waves of sectarian violence and revenge attacks. And as the fighting grinds on, there is a persistent fear of a major humanitarian crisis in the coming days and weeks, as the fighting moves toward more densely populated areas.

Aid officials, noting that as many as a million people could remain in Mosul, have been preparing for a new wave of civilians fleeing the area. More than three million people in the country have already been driven from their homes because of violence.

Some families were already streaming out of Gogjali on Tuesday, according to a witness and images on local television, but it was not immediately clear how many. The Iraqi government, dropping fliers over the city and broadcasting radio announcements, has been urging civilians to stay in their homes to avert a larger humanitarian crisis.