BAGHDAD: Iraqi forces thrust into the city of Fallujah from three directions on Monday marking a new and perilous urban phase in the week-old operation to retake the militant bastion.

Led by the elite counter-terrorism service (CTS), 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 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 am (0100 GMT), started moving into Fallujah from three directions,” he said.

"There is resistance from Daesh," he added, using an Arabic acronym for the militant Islamic State group (IS).

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 US 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, which lies just 50 kilometres west of Baghdad.

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 militants 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."

Concern for civilians

In Amriyat al-Fallujah, a government-controlled town to the south of the militant bastion, civilians trickled in, starving and exhausted after walking through the countryside for hours at night, dodging IS 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.

Fallujah is one of just two major urban centres in Iraq still held by IS.

They also hold Mosul, the country's second city and de-facto militant capital in Iraq, east of which Kurdish-led forces launched a fresh offensive on Sunday.

The militants holed up in Fallujah are believed to number around 1,000.

It is not clear yet what resources IS is prepared to invest in the defence of Fallujah, which has been almost completely isolated for months, but the city looms large in modern militant mythology.

A centre of learning for Iraq's Sunni Muslim minority that has been known as "the city of mosques", it was already a spark for a nationwide rebellion in 1920 against British colonial rule.

In November 2004, the US military suffered some of its worst losses in decades during an operation dubbed Phantom Fury which saw at least 95 members of the US forces killed in fierce combat against one of IS's previous incarnations.

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

According to the government, the organisation that has sown havoc across Iraq and Syria over the past two years now controls around 14 per cent of the national territory, down from 40pc in 2014.

However, as the "caliphate" it declared two years ago unravels, IS has been reverting to its old tactics of bombings against civilians and commando raids.