Baghdad-The Iraqi army entered ISIS-held Fallujah in a major dawn offensive on Monday as it made its “final push” to recapture the city from jihadists, according to Iraqi military officials.

Troops besieged ISIS from three fronts and managed to advance into urban areas for the first time since the operation began a week ago.

Led by the elite counter-terrorism service, Iraq’s best-trained and most seasoned fighting unit, the forces pushed in before dawn, commanders said.

“Iraqi forces entered Fallujah under air cover from the international coalition, the Iraqi air force and army aviation, and they were supported by artillery and tanks,” said Lieutenant-General Abdelwahab al-Saadi, the commander of the operation.

“Counter Terrorism Service (CTS) forces, the Anbar police and the Iraqi army, at around 4am, started moving into Fallujah from three directions. There is resistance from ISIS,” he said.

The involvement of the elite CTS marks the start of a phase of urban combat in a city where in 2004 U.S. forces fought some of their toughest battles since the Vietnam War.

The week-old operation had previously focused on retaking villages and rural areas around Fallujah, 50km west of Baghdad.

Notably, Fallujah, which survived some of the heaviest fighting of the 2003-2011 U.S.-led military intervention, was the first city in Iraq to fall under ISIS control in January 2014. In late June, 2014, the extremists declared a caliphate in territories seized in Iraq and Syria.

Only a few hundred families escaped the area ahead of the assault, with an estimated 50,000 civilians still trapped in Fallujah, sparking fears the jihadists could use them as human shields.

The families who could flee lived in outlying areas, with the biggest wave of displaced reaching camps on Saturday night.

“Our resources in the camps are now very strained and with many more expected to flee, we might not be able to provide enough drinking water for everyone,” said Nasr Muflahi, the Norwegian Refugee Council’s Iraq director.

“We expect bigger waves of displacement the fiercer the fighting gets.”

In Amriyat al-Fallujah, a government-controlled town south of the jihadist bastion, civilians ­trickled in, starving and exhausted after walking for hours at night and avoiding ISIS surveillance.

“I just decided to risk everything. I was either going to save my children or die with my children,” said Ahmad Sabih, 40.

With the help of an Iran-backed Shi’ite militia and air support from the U.S.-led coalition, the army said it had gained control of 80 percent of the towns and villages around Fallujah and was now focused on retaking the city itself.

Some 1,500 ISIS militants holed up in the center, which has been under their control for more than two years, were putting up fierce resistance with suicide bombings and rocket attacks.

A mother who fled with her husband and six children over the weekend said: “When the attack on Fallujah started, ISIS forced us to leave our homes and kept moving us from one damaged, deserted house, to another. All the time we were exposed to the exchange of fire.

“The afternoon of our last day there, the fighting became too fierce; they were shooting above our heads,” she said from a refugee camp run by the Norwegian Refugee Council 15 miles from Fallujah.