Baghdad-based military spokesman Colonel Chris Garver said Iraqi counterterrorism fighters, commandos and federal police units are now inside the city's southern edge, but stressed that progress remains slow.
"They have a foothold in the southern corner or the southern edge of the city. But it's been a significant fight to grab that foothold, and so they're continuing to try to expand," he said in a video call with Pentagon reporters.
Fallujah is a medium-sized, densely developed town that lies only 30 miles (50 kilometers) west of Baghdad.
Along with Mosul, it is one of the last two major Iraqi cities still under IS group control.
Iraqi security forces , supported by US-led coalition air strikes and advisors, have been fighting to retake the city for more than three weeks.
"It's a tough fight and it gets tougher the closer you get into the city, the harder it gets," he said.
"The distances that they move on a daily basis, the closer they get in, they get smaller and the meters that you gain become tougher to gain, they become more significant as we get them."
The IS group's systematic use of civilians for human shields has helped hamper progress against the massively outnumbered jihadists .
IS group fighters have killed dozens of civilians as they tried to flee Fallujah despite the Iraqi army's creation of an evacuation corridor for residents.
"For the most part," however, people are being treated with respect, Garver said.