BAGHDAD — When Iraq’s top generals finalized the plan to retake Mosul from the Islamic State, they gave themselves six months to finish the job.

‘‘It was the maximum time cap,’’ Prime Minister Haider al-Abadi said last week. ‘‘We had to plan for the worst, so we don’t get surprised.’’

Six weeks into the battle, the force made up of 50,000 troops, Shi’ite and Sunni tribal militias, and Kurdish fighters is a long way from winning back the country’s second-largest city.

The fight is showing the limitations of Iraq’s military and security forces, suggesting it has still not fully recovered from the collapse it suffered two years ago in the face of the militants’ blitz across much of northern and western Iraq.

As expected, ISIS militants are tenaciously defending their last major foothold in Iraq, and the 1 million civilians who remain inside are preventing the use of overwhelming firepower.

But what is alarming, according to Iraqi field commanders, is that the progress so far has been lopsided.

The battle-seasoned special forces are doing most of the fighting and slowly advancing inside the city. Other military outfits are halted outside the city limits, unable to move forward because of resistance, battle fatigue, inexperience, or lack of weapons for urban warfare.

Another major challenge for the Iraqis is the command of large and disparate forces maneuvering for a coordinated assault on a large city, according to retired US Army Lieutenant General Mark P. Hurtling, the top American soldier in northern Iraq during the troop surge of 2007-2008.

‘‘This will continue to be a tough fight,’’ he said. Many of the Iraqi army commanders are seasoned, but ‘‘most of the soldiers are young, new, and have not experienced combat.’’

The special forces are under considerable pressure to push on, slugging it out through treacherously narrow streets and alleys while enduring a daily barrage of suicide bombings and mortar and rocket shells.

As policy, the Iraqi military does not release casualty figures, but special forces’ officers speak privately of scores killed and wounded.

The main hospital treating trauma victims from the battle is overflowing with civilian and military casualties, according to Dr. Marwan Ghafuri of the West Irbil Hospital, the main triage center for trauma cases from Mosul.

He said his facility is admitting up to 150 new patients per day and he expects the influx to continue at the same level for the next three months.

The ISIS militants are putting up resistance not seen in past major battles with the Iraqi military north and west of Baghdad. They are drawing on a vast arsenal of weapons, while fighting in a city they called home for the past two years.

The militants have also dug an elaborate network of tunnels, some as long as 3,000 yards, that offer cover from drones.

‘‘We must continue to advance because we suffer fewer casualties than if we hold still and wait for other units to advance in their sectors,’’ said Brigadier General Haider Fadhil of the special forces. ‘‘We are trying to advance cautiously to minimize casualties, and we are convinced that we will eventually be asked to liberate the western sector of the city when we are done here.’’

That may be a while yet.

The special forces have driven ISIS militants from about 15 of eastern Mosul’s estimated 39 neighborhoods, some of which are no more than a handful of blocks. Their progress to date places them about 2 miles from the Tigris River, which divides the city in half.

It’s a deceptively short distance: The area is densely built up and heavily populated, and the men are advancing on multiple fronts, constantly assigning valuable resources to securing their flanks and rear as they capture more territory.

For example, in a week of fighting, they have only taken about 60 percent of the large and densely populated Zohour neighborhood, site of one of Mosul’s busiest food markets.

Mosul’s eastern half has a greater population than the western half. In a positive note, coalition airstrikes that cut off the city’s four bridges across the river have helped reduce the number of car bombs, commanders say.

In contrast, the regular forces, which have been battling for weeks through towns and villages on the way to the city, are now stalled on the edges.