Iraqi forces buoyed by the first US-led coalition air strikes on Tikrit have made a final push to flush diehard jihadists out of Saddam Hussein's hometown.

Washington had been reluctant to get directly involved in a battle to retake the town, but the Pentagon now seems keen to reassert itself as Baghdad's chief partner in the war against the Islamic State group.

The operation to retake Tikrit was launched on March 2 but failed to dislodge a relatively small number of IS fighters who have hemmed themselves in with thousands of bombs for a last stand in the city centre.

Iraqi air strikes had, by Baghdad's own admission, not been efficient and accurate enough to break the back of IS resistance.

"Now the operation to take Tikrit really begins," one US defence official told AFP.

Lieutenant General James Terry, who oversees the command in charge of the US war effort, said precision strikes would save "innocent Iraqi lives while minimising collateral damage to infrastructure".

The exact number of civilians trapped inside Tikrit is unclear but a Red Crescent spokesman last week said "no more than 30,000, probably quite a bit less".

The US military said the first wave of coalition air raids consisted of 17 strikes that struck buildings, bridges, checkpoints, staging areas, berms and a command post.

Washington had expressed strong reservations over the leading role played in the Tikrit operation by Shi'ite militia groups, some of which have been accused of serious abuses.

But the Pentagon has insisted that Washington remains Baghdad's most precious partner in the war to reclaim the vast regions of Iraq IS conquered last summer.

Lloyd Austin, a top US general, told US politicians on Thursday that Shi'ite militias "have pulled back" from the front and that special forces and police were "clearing" Tikrit.

A US condition for the strikes was that Iraq's government be "in charge" of all forces in the assault, he said.

The four-star general said the offensive had been flawed because some of the forces were previously "not supervised".

Tikrit was the hometown of executed dictator Saddam Hussein, remnants of whose Baath party collaborated with IS last summer.

It is seen as a key stepping stone to recapturing Iraq's second city Mosul, the jihadists' largest hub.