Iraqi security forces have battled the last remaining pockets of Islamic State (IS) militants in Tikrit and are close to gaining full control of the city, the country's interior minister said.

The remarks came a day after the Iraqi forces, with Shiite militias who rejoined the fight, pushed into the centre of Saddam Hussein's hometown, hoisting the Iraqi flag over the Salahuddin provincial headquarters in Tikrit and moved to control the entire city.

The objective, interior minister Mohammed Salem al-Ghabban said, is now to free all of Tikrit and restore normalcy as quickly as possible.

"There are only a few pockets of resistance left and we will announce the good news within the coming hours that these pockets of resistance are eliminated," he told reporters at the frontlines in the city.

He said the government will help displaced residents return and that a civil defence unit will be combing the city for roadside bombs and car bombs.

"After clearing the area from roadside bombs and car bombs, we will reopen police stations to restore normalcy in the city, and we will form committees to supervise the return of people displaced from their homes," Mr al-Ghabban said.

"Daesh is completely defeated," he added, using an Arabic name for the group.

The battle for Tikrit is seen as a key step toward eventually driving the militants out of Mosul, Iraq's second-largest city that is farther north.

Extremists from IS seized both cities last summer during their lightning advance across northern and western Iraq.

Iraqi forces, including the military, federal police, Shiite militias and Sunni tribes, launched a large-scale operation to recapture Tikrit on March 2 and the US launched airstrikes on the embattled city last week at the request of the Iraqi government.

Iraqi security forces have fired on snipers burrowed in high buildings and searched homes to capture or kill any remaining militants.

Soldiers fanned out in circles from the charred skeletal remains of the Salahuddin provincial government complex, captured on Tuesday.

Militant mortar fire, which had been intense over previous days, fell silent with commanders saying only a few militant snipers remain in the city.