BAZWAYA, Iraq—Iraqi security forces entered Mosul on Tuesday, with the crackle of gunfire in densely populated neighborhoods signaling a dangerous new stage of urban combat for control of the Islamic State-held city.

Iraqi forces coming from the east advanced within the city limits in the early afternoon, a U.S. official said. Other troops pressured militants from the south, as did Shiite militias to the west, tightening the military cordon around Mosul and outlying towns and villages.

The...