Tikrit, which holds both strategic and symbolic significance in the flight against IS, has been the scene of heavy fighting in the last week.
The offensive involves a combined force of more than 30,000 pro-government fighters and, if it succeeds, will be a major step in the move towards Mosul, which IS seized in June 2014, the New York Times reported.
Though the US is not directly involved in the Tikrit operation, American officials have expressed their discomfort with the prominent role of Shiite militias and Iranian military officials in the operation to take back a predominantly Sunni city, according to the Times.
Previous announcements of victory for Iraqi forces have proven premature, the Times noted, in particular in parts of Anbar Province and at an oil refinery near Baiji.