An Iraqi Shiite fighter fires artillery during clashes with ISIS militants near Fallujah, Iraq, May 29, 2016.

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

A Reuters TV crew about a mile (about 1.5 km) from the city’s edge said explosions and gunfire were ripping through Naimiya, a largely rural district of Fallujah on its southern outskirts.

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

The unit advanced another mile northward, stopping about 500 meters (yards) from the al-Shuhada district, the southeastern part of city’s main built-up area, army officers said.

The battle for Fallujah is shaping up to be one of the biggest ever fought against ISIS, in the city where US forces waged the heaviest battles of their 2003-2011 occupation against the militant group’s precursors.

Fallujah is ISIS’s closest bastion to Baghdad, and believed to be the base from which the 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 blew themselves up in the capital. Along with another bomb planted in a car, they killed more than 20 people and injured more than 50 in three districts of Baghdad, police and medical 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 50 km (30 miles) west of Baghdad.

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

On Monday, army units were “steadily advancing” to Fallujah’s southern outskirts under air cover from a US-led coalition helping to fight against the militants, according to a military statement read out on state TV.

A Shi’ite militia coalition known as Popular Mobilisation, 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.

Between 500 and 700 militants are in Fallujah, according to a US military estimate. The US-led coalition conducted three air strikes near Fallujah over the past 24 hours, destroying fighting positions, vehicles, tunnel entrances and denying the militants access to terrain, it said in a statement.

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

Fallujah, 50 kilometres west of Baghdad, is one of the two remaining major Iraqi cities still in ISIS hands.

Fighters from Iraqi Shiite group Kataib Sayyid al-Shuhada gather near Fallujah, Iraq, May 23, 2016.

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