The head of a Shia militia brigade, fighting alongside government forces, said that IS militants still held about 70% of Tikrit’s town centre.
The Shia leader expressed optimism that Tikrit would be “liberated,” even if it required street-to-street fighting.
Soldiers and militiamen have reportedly retaken key sites, including a Police headquarters and a hospital.
Muain al-Khmdy, a commander of the Iranian-backed Badr Brigade, said that pro-government forces would surround IS-held areas of the city and then attack, aiming to drive IS fighters from their location.
Several hundred militants are believed to be operating in Tikrit, research revealed.
The pro-government force ranged against them includes about 3,000 Iraqi troops with 20,000 Shia militiamen and a much smaller force of Sunni tribesmen.
Earlier, Iraqi Defence Minister, Khaled al-Obedi stated that recapturing Tikrit could be a turning point in the battle against IS.
The Defence minister 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,” Khaled said.
Tikrit was the home town of ousted former leader Saddam Hussein.
Anti-government Sunnis loyal to Saddam’s Baath party collaborated with the militants when they overran a huge swathe of Iraq, including Tikrit, last June.
The large role of Iranian-backed Shia fighters in the battle for Tikrit has raised fears of reprisals against the mainly Sunni population.
US officials are said to be concerned at reports that Shia militias have been setting fire to buildings as they advance.