Defence correspondent Jonathan Beale travelled to Tikrit with the Shia "Badr Brigade" militia
Iraqi government forces are advancing into Tikrit on several fronts, forcing Islamic State (IS) militants to fall back to the city centre, officials say.
Soldiers and militiamen have reportedly retaken key sites including a police headquarters and a hospital.
Iraq's defence minister said Tikrit's recapture could serve as a "launch pad" for further operations against IS.
It is the biggest offensive against IS mounted by the government since the jihadist group's rise last June.
The battle for Tikrit - Saddam Hussein's hometown - appeared to be entering a critical phase on Thursday.
About 3,000 Iraqi soldiers and police made a final push for the city, backed by 20,000 Popular Mobilisation Shia militiamen and a much smaller force of Sunni tribesmen.
'Turning point'
The Iraqi Defence Minister Khaled al-Obedi told the BBC that recapturing Tikrit could be a turning point in the battle against IS.
He described the city as a stepping stone to other IS-held territory, including Mosul - the country's second largest city.
"The liberation of this city [Tikrit] and province will serve as a launch pad for reclaiming the north and the west of Iraq," he said.
"If Islamic State is defeated here, they'll be defeated easily in other regions."
A suicide bomber blew up an explosive-packed car near an army position on the southern edge of Tikrit
Iranian-backed Shia militiamen are leading the offensive against Islamic State in Tikrit
On Thursday, a security official in the Samarra Operations Command in Salahuddin province told the BBC government forces had taken the Industrial Zone and Celebrations Square near the city centre after seizing the Qadisiya area further north.
The official said battles with IS militants were taking place near Celebrations Square, in the western district of al-Zuhur, and around the presidential palace complex built by Saddam in the south-east.
The Iraqi troops have been hoisting both the national flag and the flags of Shia Islam on their Humvees, the BBC's Ahmed Maher in Tikrit reports.
They are still held back from the centre by roadside bombs and booby-trapped cars, our correspondent says.
Fears for Sunnis
A senior Popular Mobilisation commander, Moeen al-Kadhimi, told CNN, external 75% of Tikrit was back in government control. The remaining 25% was in the hands of about 150 IS militants, he added.
US officials are reportedly concerned about reports Shia militia have been setting fire to buildings as they advance, Reuters reported, citing anonymous sources.
On Wednesday, the chairman of the US Joint Chiefs of Staff, Gen Martin Dempsey, said he had "no doubt" the operation would succeed, but voiced concerns about what would happen to the city's Sunni population when the fighting was over.
Iraq's defence minister said he expected troops to reach the centre of Tikrit within three to four days
Human rights activists have urged the government to protect civilians from revenge attacks by Shia militia
Shia militia leaders have vowed to seek revenge for the massacre by IS fighters and allied Sunni tribesmen of at least 700 soldiers, most of them Shia, at Camp Speicher outside Tikrit last June.
The offensive on Tikrit is the first attempt to push out IS from a major urban centre in Iraq and is seen as a test for a planned operation to retake Mosul.
Popular Mobilisation
The Popular Mobilisation (al-Hashd al-Shaabi), comprising dozens of Shia militias, takes a lead role in Iraqi operations against IS. Its fighters have also been accused of committing atrocities and acting with impunity
It was formed by the Shia-led government in June 2014 after the army collapsed in the face of an advance by IS across northern Iraq
Iran provides funding, weapons and military advisers to the Popular Mobilisation militias and reportedly controls several of them directly
The Popular Mobilisation is headed by Jamal Jaafar Mohammed, also known as Abu Mahdi al-Mohandis, a former Badr Organisation commander who is close to Iranian General Qassem Soleimani
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