BAGHDAD (Reuters) - The U.S.-backed offensive to crush Islamic State in its last major city stronghold in Iraq entered a second month on Thursday as forces arrayed against the hardline Sunni group sought finally to seal off Mosul from all sides.

The militants have been steadily retreating from areas around Mosul into the city since the battle started on Oct. 17, with air and ground support from a U.S.-led coalition.

An elite army unit, the Counter Terrorism Service, breached the city’s eastern limits for the first time two weeks ago. Other army units have yet to enter from the northern and the southern sides.

Another breakthrough came on Wednesday, when Iranian-backed militias announced the capture of an air base west of Mosul, part of their campaign to choke off the route between the Syrian and Iraqi parts of the caliphate Islamic State declared in 2014.

The capture of the Tal Afar base also offers the mainly Shi’ite forces a launchpad for operations against Islamic State targets inside Syria, and highlights the potential for the Mosul operation to reshape strategic power across northern Iraq.

To the east of Mosul, Kurdish peshmerga forces are also taking territory well outside the traditional borders of their autonomous region.

The offensive to take Mosul, the largest city under Islamic State control in either Iraq or Syria, is turning into the biggest battle in Iraq’s turbulent history since the U.S.-led invasion that toppled Saddam Hussein in 2003.

Iraqi authorities have declined to give a timeline for recapture of the whole city, but it is likely to last for months. The militants have launched waves of counter-attacks against advancing forces, tying them down in lethal urban combat in narrow streets still full of residents.

The city’s capture is seen as crucial towards dismantling the caliphate, and Islamic State leader Abu Bakr al-Baghdadi, believed to have withdrawn to a remote area near the Syrian border, has told his fighters there can be no retreat.

Iraqi military estimates put the number of Islamic State fighters in Mosul at 5,000 to 6,000. Facing them is a 100,000-strong coalition of Iraqi government forces, Kurdish fighters and Shi’ite paramilitary units.

The group seems to have retained its ability to strike across Iraq, even in central areas near Baghdad, despite the battle of Mosul.

Slideshow ( 15 images )

A suicide bomber detonated a car laden with explosives at a wedding in a Sunni town west of Baghdad on Thursday, killing 12 people and wounding 35, police sources said.

The attack appeared to have targeted Sunni provincial officials opposed to Islamic State who were attending the wedding in the town of Ameriyat Falluja, they said.

MILITANTS PROVE RESILIENT

Iraqi authorities have not published a casualty toll for the Mosul campaign overall - either for security forces, civilians or Islamic State fighters. The warring sides claim to have inflicted thousands of casualties in enemy ranks.

Nearly 57,000 people have been displaced because of the fighting, moving from villages and towns around the city to government-held areas, according to U.N. estimates.

The figure does not include the thousands of people rounded up in villages around Mosul and forced to accompany Islamic State fighters to cover their retreat towards the city.

In some cases, men of fighting age were separated from those groups and summarily killed, according to residents and rights groups. Human Rights Watch said on Thursday more than 300 former police officers were likely killed last month and buried in a mass grave near the town of Hammam al-Alil, south of Mosul.

Government forces are still fighting in a dozen of about 50 neighborhoods on the eastern part of Mosul, which is divided by the Tigris River that runs through its center.

The militants are dug in among the civilians as a defense tactic to hamper air strikes, moving around the city through tunnels, driving suicide car bombs into advancing troops and hitting them with sniper and mortar fire.

The resilience of Islamic State’s defenses has forced a greater involvement from the coalition made up mainly of western nations including Britain, France, Italy, Canada and Australia.

Slideshow ( 15 images )

CANADIANS IN COMBAT

Canadian military trainers operating with the Kurdish fighters have clashed several dozen times with Islamic State militants over the last month, defense officials said on Wednesday in Ottawa.

On three occasions, the troops were forced to use anti-armor rockets to destroy suspected car bombs, said Major-General Michael Rouleau, commander of Canada’s special forces.

The revelation could be awkward for Canada’s Liberal government, which promised that the 200-strong training force would not take part in active combat.

The United States has also deployed Apache helicopters to support Iraqi troops engaged in urban warfare in eastern Mosul.

The forces taking part in the fighting have different and sometime conflicting agendas that could complicate the continuation of the battle or the stabilization of the region of Mosul after Islamic State’s defeat.

NINEVEH IS MOSAIC

The Nineveh region surrounding Mosul is a mosaic of ethnic and religious communities - Arabs, Turkmen, Kurds, Yazidis, Christians, Sunnis, Shi’ites - though Sunni Arabs comprise the overwhelming majority.

The autonomous Kurdistan Regional Government (KRG) suggested on Wednesday it would try to expand the area it rules in northern Iraq to include surrounding villages and towns captured by Kurdish fighters from Islamic State, and possibly the oil-rich region of Kirkuk.

Kurdish peshmerga forces “will not retreat from areas retaken” from Islamic State militants in Iraq, Kurdistan President Massoud Barzani said, according to Rudaw TV station.

Barzani’s comment riled the central government in Baghdad, which opposes any plans to expand the Kurdish autonomous area.

Prime Minister Haider al-Abadi’s office said there was agreement between the government and the Kurds that provides for their “withdrawal to the places they held before the start of the liberation operations”.

But it said the agreement did not cover territory taken by peshmerga fighters from Islamic State forces between 2014 and the start of the Mosul campaign last month, which includes the contested region of Kirkuk.