Iraqi security forces ride in a military vehicle near Fallujah May 30, 2016. Reuters/Alaa Al-Marjani

The Iraqi army stormed to the southern edge of Fallujah under U.S. air support Monday and captured a police station inside the city limits, launching a direct assault to retake one of the main strongholds of Islamic State group militants.

A Reuters TV crew about a mile from the city’s edge said explosions and gunfire were ripping through Naimiya, a district of Fallujah on its southern outskirts.

An elite military unit, the Rapid Response Team, seized the district’s police station at midday, state television reported.

The battle for Fallujah is shaping up to be one of the biggest ever fought against Islamic State group, also known as either ISIL or ISIS, in the city where U.S. forces waged the heaviest battles of their 2003-2011 occupation against the Sunni Muslim militant group’s precursors.

Fallujah is the ISIS bastion closest to Baghdad and believed to be the base from where the extremist group has plotted an escalating campaign of suicide bombings against Shiite civilians and government targets inside the capital.

As government forces pressed their onslaught, suicide bombers driving a car and a motorcycle and another bomb planted in a car killed more than 20 people and wounded more than 50 in three districts of Baghdad, medical and police sources said.

Separately, Kurdish security forces announced advances against ISIS in northern Iraq, capturing villages from militants outside Mosul, the biggest city under militant control.

The Iraqi army launched its operation to recover Fallujah a week ago, first by tightening a six-month-old siege around the city 30 miles west of Baghdad.

In the heartland of Sunni Muslim tribes who resent the Shiite-led government in Baghdad, Fallujah was the first Iraqi city to fall to the Islamic State group in January 2014. Months later, ISIS overran wide areas of the north and west of Iraq, declaring a caliphate including parts of neighboring Syria.

Monday, army units advanced to the city’s southern entrance, “steadily advancing” under air cover from the U.S.-led coalition helping to fight the militants, according to a military statement read on state TV.

A Shiite militia coalition known as Popular Mobilization, or Hashid Shaabi, was seeking to consolidate the siege by dislodging militants from Saqlawiya, a village just to the north of Fallujah.

The militias, who took the lead in assaults against ISIS in other parts of Iraq last year, have pledged not to take part in the assault on the mainly Sunni Muslim city itself to avoid aggravating sectarian strife.

Militant Stronghold

Fallujah has been a bastion of the Sunni insurgency that fought both the U.S. occupation of Iraq and the Shiite-led Baghdad government that took over after the fall of dictator Saddam Hussein, a Sunni, in 2003.

American troops suffered some of their worst losses of the Iraq War there in two battles in 2004 to wrest it back from al Qaeda in Iraq, the insurgent force now known as the Islamic State group.

The latest offensive is causing alarm among international aid organization over the humanitarian situation in the city, where more than 50,000 civilians remain trapped with limited access to water, healthcare and food.

Fallujah is the second-largest Iraqi city still under control of the militants, after Mosul, their de facto capital in the north that had a prewar population of about 2 million.

It would be the third major city in Iraq recaptured by the government after Tikrit, Saddam’s hometown, and Ramadi, the capital of Iraq’s vast western Anbar province.

Fallujah is also in Anbar, located between Ramadi and Baghdad, and capturing it would give the government control of the major population centers of the Euphrates River valley west of the capital for the first time in more than two years.

On the northern front, the security forces of the autonomous Kurdish region launched an attack Sunday to oust the militants from villages about 13 miles east of Mosul so as to increase the pressure on ISIS and pave the way for storming that city.

Known as peshmerga, the Kurdish forces have retaken six villages in all since attacking ISIS positions Sunday with the support of the U.S.-led coalition, the Kurdistan Region Security Council said Monday. That represents most of the targets of their latest advance.

Iraqi Prime Minister Haider al-Abadi hopes to recapture Mosul this year to deal a decisive defeat to ISIS.

Abadi announced the onslaught on Fallujah May 22 after a spate of bombings that killed more than 150 people in one week in Baghdad, the worst death toll there so far this year. The worsening security in the capital has added to political pressure on Abadi, who is struggling to maintain the support of a Shiite coalition amid popular protests against an entrenched political class.

The bombings Monday targeted two densely populated Shiite districts, Sadr City and Shaab, and a government building in one predominantly Sunni suburb, Tarmiya, north of Baghdad.

A car bomb in Shaab killed 12 people and wounded more than 20, while in Tarmiya eight were killed and 21 wounded by a suicide bomber who pulled up in a car outside a government building guarded by police. In Sadr City, a suicide bomber on a motorcycle killed three people and wounded nine.