At the end of a meeting in Washington on Friday, France said Washington had to give up control over local forces while Italy said a new Iraqi government had to have a say over US-occupation troop's tactics.
In a nod to Iraqi authority, Secretary of State Colin Powell said the United States would withdraw its troops if the interim government made such an unlikely demand.
The US-led occupation authority plans to handover power to an interim Iraqi administration on 30 June.
But Powell insisted the top US military commander in Iraq remained "free to take whatever decision he believes are appropriate to accomplish his mission."
Washington held the G-8 meeting against the backdrop of widespread outrage at US abuse of Iraqi prisoners that has fuelled anti-Americanism among Arabs and reinforced the occupation's unpopularity at home and abroad.
Critics say the symbolic transfer of sovereignty only allows Iraqis limited self-rule because the interim government will not be able to pass laws and 135,000 US troops will remain in Iraq and retain command over all local security forces.
Russia called for the new government to be "truly sovereign" and said international support for Iraq would depend only on what Iraqis wanted.
French Foreign Minister Michel Barnier said: "this government should be a sovereign government not only with all the trappings of sovereignty, but also the hard facts of sovereignty."
And Italy's Foreign Minister Franco Frattini called for an "effective transfer" in which Iraqis should be able to tell the US, for example, not to launch an attack in the flashpoint city of Falluja.