CAMP TARIQ, Iraq — The Iraqi military’s advance into Fallujah was stalled Wednesday by fierce resistance from Islamic State fighters and concerns over protecting tens of thousands of civilians still trapped inside the strategic city.

With the operation in its second week, convoys of special forces could only inch forward on the dusty southern outskirts of the city as a handful of airstrikes sent up plumes of white smoke above clusters of low buildings on the fringes of the city’s dense urban terrain.

More than 50,000 people are believed to be still inside Fallujah, and the U.N. estimated that 20,000 of them are children, warning that they face a dire humanitarian situation in addition to the risk of forced recruitment by the extremists.

In a visit to the front line, Prime Minister Haider al-Abadi noted the slow pace and emphasized the priorities of the operation were protecting civilian lives and minimizing Iraqi casualties, but he praised the progress so far as a “remarkable advance.”

Government troops will “hoist the Iraqi flag inside Fallujah in the coming few days,” vowed al-Abadi, wearing the black fatigues of the counterterrorism force.

The operation to free Fallujah from the more than two-year grip of the Islamic State was launched May 22, and it involves the Iraqi special forces, militias consisting of mainly Shiite fighters, and airstrikes carried out by a U.S.-led coalition.

Retaking the Sunni-majority city 40 miles west of Baghdad would represent a huge victory for the Iraqi government because Fallujah was one of the first major urban areas to fall to the extremists in 2014 and has been a bastion of support for militant anti-government sentiment in Iraq since the 2003 U.S.-led invasion.

A decade earlier, Fallujah was the site of some of the bloodiest urban combat between U.S. forces and al-Qaida in Iraq.