BAGHDAD — The first surprise waiting for Dr. Raja Habib Khuzai, a member of the Iraqi Governing Council, was President Bush in the flesh, telling her and other politicians that even his mother did not know he had come to Iraq for Thanksgiving. Then, on Friday, she was summoned by U.S. officials again.

An occupation official told her, "You will have another surprise," Khuzai said, and she was ushered in to meet Sen. Hillary Rodham Clinton, here to visit American soldiers and officials and to discuss the role of women in the new Iraq.

While the New York Democrat's visit was not wrapped in the same vacuum-sealed secrecy as Bush's, the back-to-back appearances by a sitting president and someone who might run for the job, were, for most Iraqis, certainly unexpected.

But while Khuzai found the visits useful, many Iraqis — though they gave Bush and Clinton points for bravery — said their visits were irrelevant. The measure for them, unlike for the American soldiers who seemed buoyed by the visits, was whether life here would change as a result.

"We don't care about visits like this, if she came or didn't come," said Nuha Hassan, 33, a mother of three. "What we care about is whether there is electricity, about whether we can send our children to school without worrying."

Still, the novelty value, especially of Bush's swoop into Iraq, was high. "Where is President Bush?" a group of Iraqis said in English to two Americans here on Friday.

During his 2 1/2-hour visit Thursday, Bush stayed inside the heavily fortified airport complex. Clinton ventured outside the complex on her trip here with Sen. Jack Reed, a Democrat from Rhode Island. She said they came mostly to see the troops, after stops in Afghanistan and Pakistan, where she met with American soldiers and leaders of those nations. Press coverage of her visit was restricted.

"I wanted to come to Iraq to let the troops know about the great job they're doing," she said, according to a pool report by The Associated Press. "There's a lot to be proud of, particularly on the ground, with our troops."

In their visits, Bush and Clinton both addressed a new plan, freighted now with some uncertainty, to speed up transferring political authority to Iraqis. Earlier this month, the Bush administration changed course to endorse indirect elections that would turn over power by June.

But this week, the most powerful cleric in Iraq, Grand Ayatollah Ali al-Sistani, said he opposed the plan, sticking by a longstanding demand for direct elections of a new government — a process likely to take longer because it would first require the complicated tasks of taking a census and drafting a constitution.

American officials and some Iraqi politicians are seeking to find a compromise with the ayatollah, who holds great influence over the majority Shiite Muslims here. Bush, in his visit, told Iraqi politicians in a brief meeting that he still preferred indirect, caucus-style elections.

"He said, 'If it's an elected government, it will take a longer time and you have this deadline at the end of June,"' said Khuzai, one of four members of the Governing Council to meet with Bush on Thursday. The council is an interim body selected by American officials to help run the nation.

Both Clinton and Reed cautioned that the new plan was risky, and Reed emphasized that a key factor was securing approval from the Shiites.

"We're caught in a dilemma, possibly of our own making," Reed said. "A quick, hasty election might bring to power a person who doesn't share the values we're trying to encourage. But the more we wait, the more it looks like an occupation."

Clinton said that she still favored sharing the authority and the responsibility of rebuilding Iraq with other nations, but was skeptical about whether that would happen.

"It will take a big change in our administration's thinking," she said. "I don't see that it's forthcoming."

Clinton ate lunch with troops from New York at a U.S. headquarters site in downtown Baghdad in a walled-off and heavily-guarded part of the city known as the Green Zone. Then she met with soldiers of the 82nd Airborne Division in southwest Baghdad. She also met with the top U.S. officials in Iraq, including the chief civilian administrator, L. Paul Bremer and Lt. Gen. Ricardo Sanchez, the commander of ground forces in Iraq, as well as with Iraqi women and aid groups.

Because the Green Zone has been hit repeatedly by mortar fire, Clinton was spending the night in Kuwait, and planned to visit the northern Iraq city of Kirkuk, a spokesman said.

Given the secrecy of Bush's visit, many Iraqis said they did not hear about it until Friday, by which time he was back at his ranch in Crawford, Texas. Several Iraqis said on Friday that they were not aware Clinton had also visited.

Some said they wished Bush had left the airport to talk to ordinary Iraqis.

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"He could have gone to the streets to feel what is happening," said Mowaffak Hussein, 44, a cashier at a restaurant. "It's better than people telling him what is happening."

Then again, he said he was not entirely sure Bush would have been safe.

A U.S. soldier was killed on Friday in the northern city of Mosul when four mortars landed in the main compound of the 101st Airborne Division, the military reported. An Iraqi employee was injured.

Since Bush declared major combat over on May 1, 184 U.S. soldiers have been killed in Iraq, according to the military's central command in Florida.

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