He said the military push started early in the morning from the south and southwest of the city, which lies around 160 kilometres north of the capital Baghdad.
The operation came as jihadists were busy on other fronts further north, where resurgent Kurdish pershmerga forces, buoyed by Western arms deliveries and US airstrikes, have gone on the offensive.
Jihadist fighters from the Islamic State group which had already occupied parts of Syria launched an offensive in Iraq on June 9 and soon took over much of the country's Sunni heartland.
Tikrit fell on June 11 and has since been controlled mostly by Sunni militant groups, including former members of Saddam's ruling Baath party.
Iraqi government forces, which folded when jihadist-led militants swept across five provinces more than two months ago, have made Tikrit one of the main targets of their fightback.
The army, with the support of Shiite volunteers, have tried and failed twice to take back Tikrit.