Iraq's prime minister has announced that his country's military forces and allied groups have driven out Islamic State of Iraq and the Levant (ISIL) fighters from the centre of Tikrit city after month-long military offensive.

In a statement on Tuesday, Prime Minister Haider al-Abbadi said troops have retaken neighbourhoods on the southern and western edges of Tikrit and are moving to control the entire city.

He hailed the "liberation of Tikrit", congratulating the forces that took part in the battle.

Abbadi's spokesman Rafid neighbourhoods told the AFP news agency: "Iraqi forces reached the centre of Tikrit, raised the Iraqi flag and are now clearing the city."

In their push from southern Tikrit, security forces and paramilitary fighters retook the governor's headquarters and the main hospital, which had been occupied by ISIL.

But the fight to full control of the home city of former ruler Saddam Hussein continues - as the rebels still control several neighborhoods. Street-to-street fighting raged afternoon and estimates on how much of Tikrit Iraqi forces held widely differed.

Reuters journalists travelling with the police passed houses scarred by bullets, mortars and rockets as well as five or six corpses that security officers said were ISIL fighters.

The US Defense Department said it could confirm Iraqi security forces' "advancement into Tikrit to liberate the city centre as well as other parts of the city" from ISIL.

Tikrit, the capital of Salahuddin province, was seized last June by ISIL fighters as they captured territory across northern Iraq.

Tuesday also saw armed Shia groups return to the battle to aid Iraqi forces after suspending operations last Thursday when US-led air strikes were requested by Abbadi.

The US government, which mistrusts the pro-Iranian Shia forces, has sought ways to participate in the Tikrit battle without acknowledging working with forces allegedly backed by Tehran.

US officials have insisted on an Iraqi government military command for the fight, even as Shia groups remain the strongest presence on the ground, Reuters said.

Source: Agencies