Iraq's Counter-Terrorism Service is fighting "for the (Maamun) Flats area, which is considered very important for control of the Baghdad road and the surrounding neighbourhoods," Staff Lieutenant General Abdulghani al-Assadi told AFP.
"The resistance is violent and fierce because they're defending this line and this line, in our opinion, is the main line for them," said Assadi, a top CTS commander.
The damage in the Maamun area is heavy, with homes destroyed, roads cratered and rows of crumpled cars, some of them piled one on top of another.
IS overran large areas north and west of Baghdad in 2014, but Iraqi forces backed by US-led coalition air strikes and other support have since regained much of the ground they lost.
Iraqi forces launched a massive operation to retake Mosul -- the last IS-held city in the country -- on October 17, first recapturing its east before setting their sights on the smaller but more densely populated west.