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Four Iraqi soldiers were killed in street fighting with so called Islamic State militants in Tikrit overnight as they advanced slowly into the city in the wake of coalition air strikes, a security official said.

The troops entered Tikrit's southern Shishin and northern al-Qadisiya neighbourhoods on Friday, after the US-led alliance carried out air strikes against Islamic State, the officer from the Salahuddin province operation command told the Reuters news agency on Saturday. 

The campaign was slowed on Friday evening by clashes with Islamic State that killed of four and wounded 11 other soldiers, the security official said, speaking on condition of anonymity. 

The force of more than 20,000 fighters and military personnel, the majority of them from Iranian-backed Shia militias, launched the offensive on March 2, but it stalled two weeks ago, with officials citing high casualties among the fighters and concerns about civilians trapped in the city.  Iraqi military commanders called for coalition air strikes to break the deadlock, but militia leaders said they did not need help, least of all from the United States.  

Sunnis have accused the Shia militia fighters of displacing civilians and carrying out extra-judicial killings in areas they have liberated from Islamic State, including in eastern Diyala province and the farmlands surrounding Baghdad. 

The decision by Prime Minister Haider al-Abadi to request US-led air strikes on Tikrit came even though many Iraqi politicians believed he could not risk going against the wishes of the paramilitary fighters on the ground.  

US military officials, mindful of the controversy around their joining a fight in which Iran has provided critical military support, have describe the ground offensive as involving Shia fighters not aligned with Iran.

'Major sacrifices' 

Retaking the city of Tikrit, where militants have rigged streets and buildings with explosives, will require "major sacrifices" on the part of Iraqi forces, a senior intelligence officer said Saturday.  

"The task of liberating Tikrit requires major sacrifices and street fighting, and our forces are ready for these sacrifices," the officer told AFP on condition of anonymity, indicating that the pause in operations only deferred the inevitable cost.  

Islamic State (IS) has planted bombs in streets, rigged houses and other buildings with explosives, and built defensive works including  tunnels, also booby-trapped, the officer said. 

IS spearheaded a sweeping offensive last June that overran much of Iraq's Sunni Arab heartland, and the operation to retake Tikrit is Baghdad's largest to date against the militants. 

A US-led anti-IS coalition began carrying out air strikes in the Tikrit area on Wednesday, a move that increased available firepower in the air but has at least temporarily curbed it on the ground. 

Key Iranian-backed militia forces that have done much of the heavy lifting in the drive to push IS back suspended offensive operations after the strikes began, commanders told AFP.

The Pentagon conditioned its intervention on an enhanced role for regular government forces and Friday hailed the withdrawal of "those Shia militias who are linked to, infiltrated by, (or) otherwise under the influence of Iran".

Iran had been the most prominent foreign partner in the operation, but Baghdad eventually requested the US-led strikes after the drive stalled.  

The battle has continued in the absence of the militia forces, with an army colonel saying there was heavy fighting on the southern outskirts of the city. 

The advance was slow due to bombs planted by IS but security forces have gained some ground, the colonel said.