The remains of Iraqi soldiers have been found at a mass grave in the town of Yathrib, about 170km north of Baghdad, after reportedly being killed by the Islamic State of Iraq and the Levant (ISIL) group.

An official security source told local media on Monday that a mass grave containing the remains of the troops was found in the town, with the soldiers thought to have been killed by ISIL.

The source said it was unclear how many bodies had been been discovered, but said uniforms had been found in the graves. He added that work to uncover the remains was ongoing.

The find comes as the Iraqi army, supported by Shia fighters, said it was laying "full siege" to Tikrit, north of Yathrib, with ISIL fighters now surrounded.

The military - backed by at least 20,000 Shia fighters - has been fighting to regain control of Tikrit, Saddam Hussein's hometown, one of several predominantly Sunni conurbations to fall to ISIL last year.

Khaled al-Obeidi, Iraq's defence minister, said operations to recapture Tikrit had been on hold for nearly a week, with the army trying to minimise casualties by not rushing the final assault.

"When we see that the time is right for the Tikrit alliance, we will storm in as quickly as possible," he said.

"Tikrit is under full siege. We are taking caution to not take any losses and to protect civilians in the city."

The Tikrit siege is one of the first major operations in which the US-led coalition is not taking part, with US officials saying they were not asked to participate.

Against the backdrop of the Tikrit siege, the head of a Shia armed group has criticised the Iraqi army, saying it has asked for coalition air strikes to help retake the city.

Hadi al-Ameri's remarks on Sunday pointed to a possible divide between the Iraqi army and Shia units, most of which are made up of fighters.

Iran concerns

While the US has been working to train Iraqi military brigades, it has not worked with the Shia groups, since doing so would bring them uncomfortably close to Iran, which offers significant assistance to the groups.

John Brennan, CIA director, said having the leader of Iran's elite Quds Force direct Iraqi forces against ISIL is complicating the US mission.

In an interview with Fox News on Sunday, Brennan described General Qassem Soleimani as being "very aggressive and active" in advising the Shia militias, adding that he "wouldn't consider Iran an ally right now inside Iraq".

Iranian advisers have played a prominent role on the frontlines of Iraq's Salahuddin province.

If Iraqi forces are unable to push ISIL back and recover lost territory, US President Barack Obama would be faced with a choice of accepting failure in Iraq or committing US combat troops - something both Washington and Baghdad officials have spoken firmly against.

Meanwhile, multiple bombings hit the Iraqi capital on Monday killing at least 19 people and wounded 36.

The deadliest bombing struck a busy commercial street in the Habibiya section of Baghdad's Sadr City.

At least nine people were killed there and 22 others wounded, officials said.