RAMADI — (CNN) The Iraqi military said Tuesday it was trying to recapture the center of the key city of Ramadi, a provincial capital whose fall to ISIS in the spring spurred tens of thousands of residents to flee and drew U.S. criticism about Baghdad’s ability to fight the terror group.

Iraqi ground forces, backed by coalition and Iraqi air power, began their advance toward Ramadi’s center late Tuesday morning, intending to clear it of ISIS forces, the Iraqi military said.

The operation may be slowed out of concern for civilians, as ISIS was using residents as human shields Tuesday, two officials with the country’s defense ministry said without elaborating. Iraqi air forces began dropping leaflets in Ramadi last month, urging people to leave the city ahead of the military’s advance.

CNN does not have a presence in the city and cannot confirm troop movements there.

ISIS took over Ramadi — western Iraq’s largest city and the capital of Anbar province — in May after a year of fighting there.

Ramadi has strategic importance, with Anbar being the heartland of Iraq’s Sunni Muslim population, and the city lying just 110 kilometers (about 70 miles) west of Baghdad, Iraq’s heavily fortified capital.

It also has symbolic significance. After Iraqi forces pulled out of the city in May, U.S. Defense Secretary Ash Carter questioned whether the Iraqis had the “will to fight.”

Iraqi officials, including Prime Minister Haider al-Abadi, later said Carter had bad information. But Salim al-Jabouri, speaker of the Iraqi parliament and arguably the country’s most powerful Sunni politician, said that even the Prime Minister didn’t know of the withdrawal until after it happened.

The city was one of “three R’s” identified as the core of a triple-pronged U.S. strategy against ISIS that Carter floated before U.S. lawmakers in October. The others were raids by special forces, and Raqqa, the extremists’ de-facto capital in Syria.

Ramadi residents told CNN earlier this month that leaving the city wasn’t easy, because ISIS had set up checkpoints to prevent people from leaving.

“Daesh made it very clear to all of us that anyone who tries to flee the city will be considered an apostate. And you know what they will do to an apostate,” said one resident, using an alternate name for ISIS and referring to the group’s practice of detaining and killing those who don’t accept its ideology.

The-CNN-Wire ™ & © 2015 Cable News Network, Inc., a Time Warner Company. All rights reserved. (Photo: CNN)