Italy and Poland, two major European allies in the U.S.-led coalition in Iraq, pressed for a prompt handover of power to a local government fully representing the Iraqi people.
Meanwhile, lawmakers in Ukraine rejected an opposition proposal to withdraw the country's troops from Iraq.
The rumblings from the European leaders did not indicate a radical change in the countries' Iraq policies but showed the intensity of domestic pressure amid daily reports of violence and chaos in Iraq.
Italian Premier Silvio Berlusconi (search), a close ally and friend of President Bush, said while flying to the United States on Tuesday that he wanted to be sure of "a clear turnaround" in Iraq.
His remarks came a day after Italy suffered its first combat loss in Iraq. Most Italians opposed the war, but Berlusconi insisted the cause was just and sent 3,000 troops to help with reconstruction after Saddam Hussein's ouster.
Berlusconi was meeting with U.N. Secretary-General Kofi Annan (search), and then with Bush on Wednesday. An Italian TV station interviewed him by telephone as he flew to the United States and asked him what would be on the agenda there.
"It's very clear," Berlusconi said. "We want to be certain that there is a clear turnaround in the Iraqi situation — that sovereignty really passes to the government chosen by the U.N. envoy [Lakhdar] Brahimi and that this government gives life to an assembly that is representative of the Iraqi civilization."
Berlusconi has always rejected suggestions of withdrawing Italian troops early from Iraq. But the center-left opposition here has argued against that position in recent days after attacks on Italian troops, saying a mission supposed to be about peace has become one about war.
Recent violence in Karbala and Najaf — areas where Polish troops in Iraq are based — also has increased pressure on new Polish Prime Minister Marek Belka (search).
He said Tuesday that the U.S.-appointed Iraqi Governing Council "does not have enough legitimacy," and he urged Washington to move more quickly toward returning Iraqi sovereignty.
Despite many Poles' opposition to military involvement in Iraq, Belka has vowed to remain in the coalition. Yet Belka says he hopes that political progress in Iraq will allow his nation to start withdrawing some troops early next year.
In Ukraine, demands for withdrawing troops from Iraq increased after two soldiers were killed there last month, bringing the number of combat deaths to three.
The opposition Communist Party initiated Wednesday's vote, arguing that Ukraine was facing possible terrorist attacks because of its military presence in Iraq.
At the closed-door session, lawmakers loyal to President Leonid Kuchma (search) refused to go along with the move, opposition lawmaker Mykola Tomenko said, according to the Interfax news agency.
Kuchma has dismissed calls for withdrawal.