A column of black Humvees carrying Iraqi special forces rolled into southern Fallujah on Wednesday, the first time in more than two years that government troops have entered the western city held by the Islamic State group.

The counterterrorism troops fought house-to-house battles with the militants in the Shuhada neighborhood, and the operation to retake the city is expected to be one of the most difficult yet.

“Daesh are concentrating all their forces in this direction,” said Gen. Haider Fadel, one of the commanders of the counterterrorism forces, using the Arabic acronym for the Islamic State militants.

Prime Minister Haider al-Abadi promised a swift victory when he announced the start of the operation on May 22 to liberate Fallujah, about 40 miles (65 kilometers) west of Baghdad. But the complexity of the task quickly became apparent.