Iraqi forces thrust into the city of Fallujah from three directions yesterday marking a new and perilous urban phase in the week-old operation to retake the extremist bastion.

The drive to recapture the first city to be lost from government control in 2014 came as fighting also raged in neighboring Syria, leaving huge numbers of civilians exposed. Led by the elite counter-terrorism service (CTS), Iraq's best-trained and most seasoned fighting unit, the forces pushed into Fallujah before dawn, commanders said.

"Iraqi forces entered Fallujah under air cover from the international coalition, the Iraqi air force and army aviation, and supported by artillery and tanks," said Lieutenant General Abdelwahab al-Saadi, the commander of the operation. "CTS forces, the Anbar (provincial) police and the Iraqi army, at around 4:00 a.m., started moving into Fallujah from three directions," he said.

"There is resistance from DAESH," he added.

CTS spokesman Sabah al-Noman told AFP: "We started early this morning our operations to break into Fallujah."

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 rural areas around Fallujah, which lies just 50 kilometers west of Baghdad. It had been led by the Hashed al-Shaabi paramilitary force, which is dominated by Tehran-backed Shiite militias.

They were still in action Monday, attempting to clear an area northwest of Fallujah called Saqlawiya, officers said.

Only a few hundred families have managed to slip out of the Fallujah area ahead of the assault on the city, with an estimated 50,000 civilians still trapped inside, sparking fears the extremists could try to use them as human shields.

The only families who were able to flee so far 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 to the south of the extremist bastion, civilians trickled in, starving and exhausted after walking through the countryside for hours at night, dodging DAESH surveillance.

"I just decided to risk everything. I was either going to save my children or die with my children," said Ahmad Sabih, 40, who reached the NRC-run camp early on Sunday.

A senior police commander said his forces had assisted 800 civilians fleeing areas north of Fallujah on Monday. Fallujah is one of just two major urban centers in Iraq still held by DAESH extremists.

The extremists holed up in Fallujah are believed to number around 1,000. It is not yet clear what resources DAESH is prepared to invest in the defense of Fallujah, which has been almost completely isolated for months.

Fallujah, which is about 65 kilometers west of Baghdad, is one of the last major DAESH strongholds in western Iraq. The extremist group still controls territory in the country's north and west, as well as Mosul, Iraq's second-largest city.

Fallujah is expected to give Iraqi forces one of their toughest battles yet but DAESH has appeared weakened in recent months and has been losing territory consistently over the past year.

According to the government, the organization that has sewn havoc across Iraq and Syria over the past two years now controls around 14 percent of the national territory, down from 40 percent in 2014. However, DAESH has been reverting to its old tactics of bombings against civilians and commando raids.

In other developments, Baghdad witnessed three deadly attacks Monday morning that killed and injured dozens.

The bombings by DAESH, which has been behind several recent deadly attacks in Baghdad and beyond, are seen as an attempt by the militants to distract the security forces' attention from the front lines.

The deadliest of Monday's attacks took place in the northern, Shiite-dominated Shaab neighborhood of Baghdad where a suicide bomber rammed his explosives-laden car into a checkpoint next to a commercial area, killing eight civilians and three soldiers. The explosion also wounded up to 14 people, a police officer said.

A suicide car bomber struck an outdoor market in the town of Tarmiyah, about 50 kilometers (31 miles) north of Baghdad, killing seven civilians and three policemen, another police officer said, adding that 24 people were wounded in that bombing.

And in Baghdad's eastern Shiite Sadr City district, a bomb motorcycle went off at a market, killing three and wounding 10, police said. Medical officials confirmed casualty figures. All officials spoke on condition of anonymity as they were not authorized to release information.

DAESH claimed responsibility for the three attacks in a statement circulated on social media that could not be independently verified by dpa.