Iraqi forces need support from coalition air strikes in Tikrit, where die-hard jihadists are defending their last redoubt with trenches, sandbags and roadside bombs, a top officer said on Sunday.

Two weeks into Baghdad's biggest operation yet against the Islamic State (IS) group, Iraqi forces have a complete stranglehold on Tikrit but have yet to launch a final assault.

Staff Lieutenant General Abdulwahab al-Saadi said he had asked the defence ministry to request coalition involvement, but "no air support" from foreign allies had yet been provided in Tikrit.

That assertion is supported by daily statements from the coalition that have not mentioned strikes in the area.

Asked if US-led coalition air strikes would help, Saadi said: "Of course... the Americans have advanced equipment, they have AWACS (surveillance) aircraft."

"They are able to locate the targets exactly" and carry out accurate strikes, he told AFP in an interview at Tikrit University on the northern edge of the city.

"With the advanced technology of the aircraft and weapons they have, of course (strikes) by them are necessary," Saadi said.

Saadi said that support from the Iraqi air force had been "limited".

Fighters from the Imam Ali Brigades, a Shiite militia involved in the Tikrit operation, complained to AFP that a Sukhoi jet had even targeted pro-government forces by mistake.

Since IS fighters took the city in June 2014, they have planted bombs underneath every road, according to residents who fled Tikrit.

One police officer gave an estimate of 10,000 IEDs (improvised explosive devices) in Tikrit.

"We are reinforcing our offensive capacities in the areas we have cleared and reinforcing our control on the entrances to the city," an army major general said Sunday.

"IS is putting up sandbags and digging trenches," he said.

Saadi said that while there were enough personnel trained in explosives disposal, there is a shortage of the equipment to carry out the task.

Karim al-Nuri, a spokesman for the volunteer Popular Mobilisation units, said on Saturday he expected Tikrit to be liberated within 72 hours.

- Iran involvement -

But the army was less upbeat, with officers saying it could be days or even up to two weeks before the city is retaken.

Saadi said he thought the reason there had been no coalition air strikes in support of the Tikrit operation was political, not military.

Shiite Iran has been Baghdad's main foreign partner in the operation and Tehran's top commander in charge of external operations, Qassem Soleimani, has been on the front lines in several battles against IS.

Officials in Washington have expressed unease at the level of Iranian involvement in the overwhelmingly Sunni city which was executed dictator Saddam Hussein's home town.

Coalition air strikes have supported several other operations to reclaim jihadist-held territory in Iraq, including some in which Iran-backed Shiite militias were involved.

Iraqi security forces, backed by Shiite volunteers and militias, and in some cases Sunni tribesmen opposed to IS, have in recent months been working their way north.

In October, they retook Jurf al-Sakhr, one of the southernmost areas to have been captured by IS, and have since also reclaimed the eastern province of Diyala.

Iranian support was crucial in both operations.

Kurdish peshmerga forces have also been pushing the jihadists back from northern parts of the country, with US-led coalition support.

The last remaining IS stronghold east of the Tigris river is Hawijah, a town northeast of Tikrit, where fleeing jihadists are believed to have gathered and on which Kurdish forces are advancing.

Tikrit is seen by commanders as a key stepping stone on the way to reconquering IS's northern hub of Mosul, Iraq's second city.

The outcome of the battle seems in little doubt, but there is more at stake for the government than just territorial gain.

The vast operation is seen as a test of Baghdad's ability to instil discipline in the array of fighting forces involved in the anti-IS war and prevent some of the abuses committed in the past.

Tens of thousands of people have been displaced by the offensive. Tikrit once had an estimated population of 200,000 but it is unclear how many civilians remain there.

Local volunteer fighters and police will hold Tikrit after it is retaken, while the army will defend the city from outside, said Saadi.

But for now, the advance is "slow and steady".

"We are preserving our units so they do not take unnecessary losses," he said.

In Baghdad, meanwhile, Iraqi intelligence said Sunday it had arrested 31 IS members responsible for planning and carrying out 52 attacks in the capital.