JOHN YANG: The Iraqi government, with United States support, stepped up the pace to retake the city of Fallujah. Iraqi military forces stormed the southern edge of the city, which has been controlled by ISIS since January 2014.

Iraqi tanks rolled down a main road leading into Fallujah, spearheading the all-out push to recapture the city. The offensive to rout ISIS militants began last week, with government forces advancing slowly to try to minimize civilian casualties. Government officials and aid groups estimate at least 50,000 people are trapped in the besieged city.

HADI AL-AMIRI, Commander, Popular Mobilization Forces (through interpreter): Our advice to our troops is to treat families gently and kindly, and to respect them. Our advice to fighters is to protect and guard public and private properties.

JOHN YANG: Fallujah, about 40 miles west of Baghdad, is one of the Islamic State's last major strongholds in the region. ISIS has controlled it since 2014. Ramadi, farther to the west, was liberated at the end of last year. It was a major victory for Iraqi forces, but at a great cost. Much of Ramadi was leveled in the process.

Fallujah may now face a similar fate. It's being bombarded by Iraqi forces on the ground and the U.S.-led coalition from the air. The city is no stranger to destruction. It was largely ruined back in 2004, after the U.S. invasion and subsequent battles with insurgents.

Maher Chmaytelli is the Reuters bureau chief in Baghdad.

MAHER CHMAYTELLI, Reuters: The population of Fallujah is — is a conservative population, It's like an Islamic Sunni, conservative, has a Sunni conservative background.

Historically, let's say, since 2003, since Saddam was toppled, Fallujah was very much like a bastion of the insurgency against first the U.S. occupation of Iraq, and later off against the Shiite-led governments that were put in place after the removal of Saddam.

JOHN YANG: Thousands have been displaced by the years of fighting, and some have been living in camps for two years. They say conditions in the city are desperate.

BAAHJET IBRAHIM, Imam from Fallujah (through interpreter): Those who are inside cannot leave and those who are outside cannot help them. I mean, there is no food at all. A sack of flour costs more than $800. And you can't even get it. Now my relatives who are still there have paid 683 U.S. dollars for 44 pounds of rice and flour.

JOHN YANG: There have been calls for the government to open a safe corridor for the injured, elderly and children to leave.

As Islamic State forces are pressed in Fallujah, they are striking back in Baghdad. Mangled wreckage was all that was left of a suicide bomber's car that detonated near a commercial area today, killing eight civilians and three soldiers.

MAN (through interpreter): By launching such attacks, the militants aimed to thwart our determination and resolution to go forward with our victories in Fallujah and Garma. Despite the casualties that we have suffered, we are ready to proceed with our battles and our military gains.

JOHN YANG: The targets in the Iraqi capital have been largely Shiites, and the Shiite-dominated government is feeling the heat.

MAHER CHMAYTELLI: Shia politicians have been pressuring the government to take action against Fallujah after the series of bombings that we have seen, especially over the pats two weeks. As soon as he announced the offensive on Fallujah, we have seen more or less the Shiite community rallying around him, participating in the battles.

JOHN YANG: Iraqi officials say they have to take Fallujah before moving on to Mosul, the country's second largest city.