Iraq's armed forces, backed by Shia militia, attacked Islamic State strongholds north of Baghdad today.

It is the start of an offensive to retake the city of Tikrit and the surrounding Sunni Muslim province of Salahuddin.

The offensive is the biggest military operation in the province since the Sunni Islamist radicals seized swaths of north Iraq last June and advanced towards the capital Baghdad.

Progress in Salahuddin will affect plans to recapture Mosul further north.

An official from the US Central Command said last month the assault on Mosul, the largest city under Islamic State control, could start as early as April.

However, Iraq has declined to confirm that timetable.

Other US officials, speaking to Reuters on condition of anonymity, suggested the Mosul operation would not likely start until later, possibly in the autumn.

In Salahuddin, Islamic State fighters control several strongholds including Tikrit, hometown of executed former president Saddam Hussein and other Tigris river towns.

A source at the local military command said forces advanced north from the government-held city of Samarra towards the town of al-Dour, an Islamic State bastion, and Tikrit, which lies about 40km north of Samarra.

Salahuddin governor Raed al-Jabouri told Al-Arabiya Al-Hadath television tonight that the army had not yet entered central Tikrit or al-Dour.

Iraq's air force carried out strikes in support of the advancing ground forces who were being reinforced by troops and militia from the neighbouring eastern province of Diyala.

But the Pentagon said the US-led coalition, which has carried out air strikes against Islamic State positions in Iraq and Syria, was not yet involved.

"We're fully aware of this operation but because the Iraqis didn't request our support for it, we're not providing support," Colonel Steve Warren said.

Artillery gunners in a military base just north of Tikrit also bombarded Islamic State positions in the city, another Iraqi source said.

But the soldiers and Shia militia fighters faced heavy opposition from Islamic State fighters who have had months to dig in, coming under attack as they advanced towards Samarra from their base to the east.

Declaring the start of operations yesterday evening, Iraqi Prime Minister Haider al-Abadi gave Islamic State supporters what he said was one last chance to lay down their arms, or face "the punishment they deserve because they stood with terrorism".

But he also stressed that the army and militia must protect civilians and property in the battlefield.

Shia militia have been accused of mass executions and burning of homes in areas they have seized from Islamic State.

Leaders of the paramilitary forces have denied the accusations.

Today’s offensive follows several failed attempts to drive the militants out of Tikrit since last June, when Islamic State declared a caliphate in the territories it controls in eastern Syria and northern and western Iraq.

In Iraq, months of US-led air strikes, backed up by the Shia militias, Kurdish peshmerga fighters and Iraqi soldiers have contained Islamic State and pushed them back from around Baghdad, the Kurdish north, and the eastern province of Diyala.

But they have held most of their strongholds in Salahuddin and taken new territory in the western province of Anbar.