Iraqi forces said on Sunday they had recaptured the site of an ancient Assyrian city blown up by the Islamic State group, as they battled the jihadists south of Mosul.

The troops pushed towards Nimrud last week as they pressed an offensive begun on October 17 to recapture Iraq's second city, which the jihadists seized along with swathes of Iraq and Syria in mid-2014.

A Kurdish-Arab alliance is pursuing a twin offensive against the other major city still under IS control, Raqa in Syria, and a US-led coalition is backing both assaults with air strikes.

"The villages of Al-Nomaniyah and Al-Nimrud and the ruins of Nimrud were recaptured," Staff Brigadier General Saad Ibrahim of the 9th Armoured Division told AFP.

Iraq's Joint Operations Command had announced earlier Sunday that the entire Nimrud area was retaken, but later said that this was incorrect.

However, the village of Nimrud and the archaeological site have been recaptured, the JOC said.

Nimrud was the one of the great centres of the ancient Middle East. Founded in the 13th century BC, it became the capital of the Assyrian empire, whose rulers built vast palaces and monuments that have drawn archaeologists for more than 150 years.

In April last year, IS posted a video on the internet of its fighters smashing monuments before planting explosives around the site and blowing it up.

It was part of a campaign of destruction against heritage sites under jihadist control that also took in Hatra in the desert south of Mosul and Palmyra in neighbouring Syria.

- Displaced civilians -

IS says the ancient monuments are idols that violate the teachings of its extreme form of Sunni Islam, but it has still sold artefacts to fund its operations.

The United Nations Educational, Scientific and Cultural Organization welcomed the news of Nimrud's recapture.

"We look forward to coordinating with the relevant authorities in Baghdad on providing support for any assessments that need to be done of the site, once the area has been stabilised," UNESCO spokesman George Papagiannis said.

The Iraqi offensive has seen federal forces and Kurdish peshmerga fighters advance on Mosul from the east, south and north.

The elite Counter-Terrorism Services (CTS) force has pushed into the eastern outskirts of Mosul, with heavy fighting in recent days.

CTS Staff Lieutenant Colonel Muntadhar Salem told AFP on Sunday that its forces were looking to move into a new eastern neighbourhood.

"Our goal today is to clear out IS from the western part of Karkukli," he said.

North of Karkukli in the Arbajiyah district, CTS forces were facing sniper fire as they moved street-to-street clearing houses.

In the Al-Samah neighbourhood, which the CTS said they have cleared, two young boys fell victim to IS mortar fire Sunday.

Shafiq, 15, died on his way to a field hospital, and 12-year-old Mohammed suffered a bad leg wound.

Mortar rounds "hit one right after the other. Mohammed and Shafiq were the first ones to fall", said their neighbour Ghassan, wiping bloodied hands on his pants.

Shafiq's grandfather, head in his hands, sobbed nearby as neighbours and relatives tried to comfort him.

The attack was a bloody reminder that residents in areas of Mosul recaptured from IS can be still very much in danger.

On the edge of Mosul, dozens of civilians could be seen walking Sunday towards a gathering point from where they would be taken to a camp for the displaced.

- Jihadist resistance -

In neighbouring Syria, the US-backed Syrian Democratic Forces (SDF) militia alliance has moved to about 30 kilometres (20 miles) from Raqa since launching its offensive a week ago.

Commanders have said the SDF is close to completing a first phase of the operation to surround and isolate Raqa before launching an assault on the city itself.

The jihadists are resisting fiercely in both Mosul and Raqa, and military commanders have warned of long and difficult battles ahead.

Turkey has launched its own operation against IS just south of its border in Syria, and a monitor said Sunday that Ankara-backed rebels had neared the IS stronghold of Al-Bab.

The rebels had moved to about two kilometres from Al-Bab, as Turkish forces targeted the town with artillery and air strikes, the Syrian Observatory for Human Rights said.

Ankara launched its unprecedented cross-border operation saying it was targeting both IS and the Kurdish People's Protection Units (YPG) militia, a key opponent of the jihadist group, that dominates the SDF.

Turkey considers the YPG a "terrorist" organisation, and wants to avoid the creation of a contiguous, semi-autonomous Kurdish zone along the Syrian border.

Kurdish forces have also played a major role in the battle against IS in Iraq.

Its autonomous Kurdish region has gained or solidified control over large areas claimed by both it and the federal government in Baghdad.

In a report on Sunday, Human Rights Watch said Iraqi Kurdish forces had demolished Arab homes and buildings in disputed areas in the north.

HRW raised concern that the destruction was "for the purpose of preventing or dissuading Arabs from returning" in order to strengthen Kurdish claims to the areas.

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