Iraqi forces battled the last jihadists in Tikrit Wednesday to seal a victory the government described as a milestone in efforts to rid the country of the Islamic State group.

Iraqi fighters picked their way through the rubble-strewn streets of the city, wary of any last-ditch attack from diehard IS fighters and of the thousands of bombs they left behind.

A major military push saw Iraqi police and allied forces retake the city centre on Tuesday but pockets of jihadist militants remained.

A top leader in the Badr organisation, one of the most prominent Shiite militias in Iraq, admitted that Tikrit had not been completely purged of jihadist fighters.

"Snipers are still there and many buildings are booby-trapped," Karim al-Nuri told AFP in the northern Tikrit neighbourhood of Qadisiya.

A commander for the Ketaeb Imam Ali militia said his men were involved in a firefight in the north of the city as late as 11:00 am (0800 GMT).

They "tried to advance on the university," Rasul al-Abadi told AFP, adding that there were "no more than 30" IS fighters left in the city's vast northern district of Qadisiya.

"The Iraqi security forces control 95 percent of the city, there are sporadic clashes," said an army lieutenant colonel from Salaheddin province, of which Tikrit is the capital.

An official from the governor's office said municipal teams were already at work in some reconquered neighbourhoods, cleaning debris and restoring power.

- Mosul planning -

On Tuesday, Prime Minister Haider al-Abadi claimed the city was liberated but the US-led coalition that has been helping Baghdad from the air said there was "still work to be done".

After fighters replaced the black jihadist flag on the provincial headquarters with Iraq's tricolour Tuesday, Abadi hailed the reconquest of Tikrit as a "historic milestone".

A paramilitary commander said IS fighters launched an attack from a mountain hideout northeast of Tikrit Wednesday in an attempt to open a safe passage to the town of Hawija for fleeing militants.

Iraq's top brass was already training its sights on Mosul, which jihadist fighters seized from the government at the same time as Tikrit in June last year.

"This victory is only a new starting point from which to launch the operation to liberate Nineveh province," the defence ministry said Tuesday after a meeting of top commanders.

The loss of Tikrit further isolates the main IS hub of Mosul, with Baghdad's forces now set to push north while Kurdish forces close in from the three other directions.

Zaid al-Ali, author of "The Struggle For Iraq's Future", said however that the fighting in Tikrit was made easier by the fact that the city was largely emptied of its population even before the operation began on March 2.

"Mosul still has a large civilian population, which will make things very complicated," the analyst said.

- US-Iran tension -

The government has provided no information on how many fighters were killed, wounded or captured in the fighting but Baghdad forces are believed to have suffered heavy casualties.

Iraqi army and police forces, as well as volunteers and Iran-backed Shiite militias, completely surrounded Tikrit within two weeks of launching the operation.

There was a lull in fighting when government forces and their allies apparently balked at the number of snipers, booby traps, berms and trenches which IS was using to defend its city centre redoubt.

Iran was Baghdad's top foreign partner in the early stages of the operation but Iraqi air strikes were proving insufficient to break the back of IS resistance.

Abadi's government eventually requested strikes from the US-led coalition which has been assisting Iraqi forces elsewhere in the country since August last year.

US jets began bombing IS targets in Tikrit on March 25.

The move sparked a freeze in the participation of the Popular Mobilisation units, an umbrella organisation for volunteers and militias which accounted for the bulk of the forces in Tikrit.

The Pentagon had expressed unease at the role played by Iran and its proxies and said it conditioned its intervention on regular forces taking the lead.

But after giving themselves political cover by declaring they do not want to work with each other, both sides took part in the operation this week.

The Iraqi government had tried and failed several times to retake the hometown of former president Saddam Hussein but the latest operation was larger and better organised.

A significant number of local Sunni tribal forces were involved in the battle to liberate Salaheddin from IS, in an effort to defuse sectarian resentment.

Amid concerns over abuses committed by Shiite fighters against Sunnis in recaptured areas, the UN's top envoy in Iraq reiterated an appeal for civilians to be protected.

"Civilians' safety and security must be protected in line with fundamental human rights principles and humanitarian law," Jan Kubis said in a statement.