Iraqi military officials say they expect to reach the centre of Tikrit in 72 hours.
Backed by their mainly Shi’ite militia allies, forces have been waging fierce battles to secure neighbourhoods of the strategic city, still in the hands of ISIL militants.
They entered the city – Saddam Hussein’s hometown – for the first time on Wednesday, from the north and south.
Officials said on Friday that their operations would be put on hold temporarily because of bombs planted by militants to hamper their progress.
ISIL has seized cities and towns across Syria and northern and western Iraq as part of their offensive.