Iraqi forces have broken through ISIL's defences inside the northern city of Tal Afar and reached the city centre, a major gain in the battle for the armed group's last urban stronghold.

US-backed forces seized the neighbourhoods of Nida', al-Nasr, Saad, and Taliaa around the Ottoman-era citadel, said a statement from the Iraqi Joint Operations Command on Friday.

Up to 2,000 battle-hardened fighters remain in Tal Afar, according to US and Iraqi military commanders.

A predominantly Turkmen district, Tal Afar was overrun by Islamic State of Iraq and the Levant (ISIL, known as ISIS) fighters in 2014. An operation to retake the city began on Sunday.

Al Jazeera's Osama bin Javaid, reporting from Erbil in northern Iraq, said there has been a rapid advancement by the Iraqi forces in the last couple of hours.

"ISIL has been putting up stiff resistance, but Iraqi security forces - including the rapid response units, the federal police, and the Iraqi army - have been able to take out these targets not just with the help of the soldiers on the ground but also air strikes and smart artillery that is backing them up by the US-led coalition."

READ MORE: Iraqi forces 'completely surround ISIL' in Tal Afar

Tal Afar is located 70km west of Iraq's second city Mosul and 150km east of the Syrian border.

It lies along the supply route between Syria and the former ISIL-stronghold of Mosul. The district has produced some of the armed group's most senior commanders.

Iraqi military spokesman General Yahya Rasool told AP news agency on Friday after taking control of several neighbourhoods, Iraqi forces are currently on the outskirts of the neighbourhood of al-Qalaa.

Earlier, a top army commander said Iraqi soldiers had captured a prominent shrine revered by Shia Muslims.

In advance of the operation, the Iraqi army had amassed some 400,000 troops and personnel in preparation for retaking Tal Afar.

'Big blow'

After the fall of Mosul last month, ISIL's control in Iraq has weakened with fighters holding small pockets in the north, centre and east of the country.

Al Jazeera's Javaid said reclaiming Tal Afar from ISIL will be a "big blow" to the armed group because of its strategic location.

"Tal Afar is at the crossroads, which is very essential for ISIL fighters to reach parts of Syria that it controls and to try to smuggle things from Turkey," he said.

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On Monday, Lise Grande, the UN humanitarian coordinator for Iraq, said more than 30,000 people had already fled the city and surrounding areas.

The Iraqi army said it believes some 10,000 civilians remain inside, adding it had secured safe corridors for them.

But many are not so sure about their safe passage out.

"People do not feel secure because they have to travel between one set of Iraqi forces to the other," said Javaid.

"And rather than make their way directly to the north they have to go through the liberated areas of western Mosul where ISIL fighters and their families are being screened."

As in the battle for Mosul, civilians are suffering. Those remaining are threatened with death by ISIL, according to aid organisations and residents who managed to flee.

People are arriving at camps for displaced people with wounds from sniper fire and mine explosions.

The spiritual leader of Iraq's Shia majority called on doctors to help civilians fleeing clashes.

Grand Ayatollah Ali al-Sistani said medical workers should travel to areas around the battle for Tal Afar to help "to treat the wounded and treat them as a humanitarian, national and religious duty".

Also on Friday, Iraqi military investigators said they discovered two mass graves near a former ISIL prison outside Mosul that contains the bodies of 500 victims.

The Media Cell Security Investigation team said in a statement one grave near the Badoush Prison contained the bodies of 470 prisoners killed by ISIL. It said a second grave contained 30 victims.

A security official, who spoke on condition of anonymity, said based on records of prisoners who were at Badoush most are believed to have been Shia Muslims or other minorities.