Iraq has launched a military operation to recapture Tikrit, the hometown of former leader Saddam Hussein, from Islamic State (IS) and its allies.
A force of about 30,000 troops and militia were said to be attacking on different fronts, backed by air strikes from Iraqi fighter jets.
Fighting is reported in towns to the north and south of Tikrit.
A Shia militia commander has told the BBC that Iran's Gen Qasem Soleimani is also taking part in the operation.
Gen Soleimani is the commander of the Iranian Revolutionary Guards' overseas operation arm, the Quds Force.
He emerged from decades in the shadows after the IS advance in Iraq last summer, personally overseeing the defence of the capital Baghdad and mobilising pro-Iranian Shia militia - by organising them as well as funnelling money and weapons to them.
Tikrit lies 150km (95 miles) north of the capital Baghdad in Salahuddin province. It was seized in June 2014 by IS militants backed by anti-government Sunni allies loyal to Saddam Hussein's banned Baath party.
A commander of a Shia militia unit involved in the offensive told BBC Persian that IS announced it had taken a number of youths hostage and threatened to kill them if government forces entered the city.
He added that the Iranians had been involved in the Tikrit operation for the past two days.
Gen Soleimani has been pictured visiting the front lines north of the capital on several occasions.
Tehran says it has only sent troops to advise Iraqi security forces, Kurdish Peshmerga fighters and Shia militiamen.
However, members of the Guards and the Quds Force are widely believed to be involved in combat operations, including those that have benefited from US-led coalition air strikes.
On Monday, Al-Iraqiya TV said IS militants had been dislodged from some areas outside Tikrit.
It added that Iraqi troops and fighters from the Popular Mobilisation Forces - an umbrella group of Shia militia fighting IS - were moving on Tikrit as air strikes hit northern militant strongholds.
There are unconfirmed reports that al-Dour, south-east of Tikrit, has been taken by Iraqi forces and fighting is also reported in the town of al-Alam, north of the city, and Qadisiya.
Government forces say they are 5km away from the heart of the city, the BBC's Ahmed Maher reports in Baghdad, but this has not been confirmed by independent sources.
Later, army and medical sources said five soldiers and 11 militia fighters had been killed by gunfire and roadside bombs.
Shia militia have done much of the fighting against IS militants but have also been accused of killing scores of Sunni civilians in apparent revenge attacks.
Analysis: Ahmed Maher, BBC News, Baghdad
The operation involving up to 20,000 government troops is being backed by an alliance of volunteers mainly from the Shia community but also Sunni tribal fighters.
The Popular Mobilisation Force was formed last summer following the collapse of army troops after IS militants swept through the Sunni heartlands in the north and west of Iraq.
The jihadist movement is backed by Sunni insurgents, who started to take up arms against the Shia-led government in late 2013 after months of protests against what the Sunni community perceived as marginalisation and discrimination.
Several governments have attempted to reclaim Tikrit, the capital city of Salahuddin province, but have failed since July 2014.
The city is also symbolic for being the birthplace of Saddam Hussein. US forces found the former president hiding in southern Tikrit eight months after the US-led invasion in 2003.
If the military operation succeeds, the government forces and their allies will face a much bigger challenge to retake the main stronghold of IS in the north, the city of Mosul.
Prime Minister Haider al-Abadi met military leaders in Salahuddin province ahead of the advance.
He declared the start of the operation late on Sunday, as tens of thousands of troops and militia gathered in the central town of Samarra.
Mr al-Abadi offered to pardon all Sunni tribal fighters "who have been misled or committed a mistake to lay down arms" and abandon IS.
He described it as a "last chance", saying that the city of Tikrit would soon be returned to its people.
IS militants hold several areas of Salahuddin, a predominantly Sunni Muslim province.
Tikrit was the second major gain for IS after the group captured the city of Mosul in June last year.
Mosul was home to more than a million people when it fell to IS after the militants launched an offensive in northern Iraq that saw it seize large swathes of the country.
Soldiers and allied Shia militiamen have now begun to recapture territory from IS north of Baghdad, with the help of US-led coalition air strikes.
At the same time, Kurdish Peshmerga forces have been making advances around Mosul.
In February, Mr al-Abadi said that Iraqi armed forces would be launching a major offensive "in a few months' time" to retake the city from IS militants.