A U.S. soldier, meanwhile, was killed when guerrillas shelled a military base in the northern city of Mosul.
Clinton and Reed said the expense and political burden in administering Iraq would be made easier with the U.N.'s stamp of legitimacy and help in transferring power to Iraqis.
"I'm a big believer that we ought to internationalize this, but it will take a big change in our administration's thinking," the former first lady said. "I don't see that it's forthcoming."
Both senators cautioned that the Bush administration's new plans to speed up the transfer of power to an Iraqi government are risky, given the country's political and social upheaval.
Reed, a Rhode Island Democrat, said a "critical factor" for coalition authorities was securing the blessing of Iraq's majority Shiite Muslim community, including Grand Ayatollah Ali al-Husseini al-Sistani, who has criticized the plan.
Al-Sistani, whose opinion is crucial to the success of any political plan in Iraq, has said in recent days he wants an elected Iraqi provisional government instead of one chosen through regional caucuses.
"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 the main purpose of her trip was to show support for U.S. troops.
"I wanted to come to Iraq to let the troops know about the great job they're doing," the New York Democrat said.
Reed, who voted against authorizing war against Iraq, said his rationale has been confirmed by his visit, as well as by a trip he made in July.
He said the Bush administration was too hasty in dismissing the U.N. search for weapons that probably would have shown that Iraq represented no imminent threat to the United States. He said alleged links between Osama bin Laden's al Qaeda terrorist network and Saddam Hussein also appeared to be exaggerated.
For her part, Clinton supported a resolution granting Bush congressional authority to wage war against Iraq.
Iraqis expressed differing opinions about the significance of Thursday's 2½-hour visit by Bush, which was organized in such secrecy that even members of the U.S.-appointed Iraqi Governing Council who greeted the president were not told about it.
"We cannot consider Bush's arrival at Baghdad International Airport yesterday as a visit to Iraq," said Mahmoud Othman, a member of the U.S.-appointed Iraqi Governing Council. "He did not meet with ordinary Iraqis. Bush was only trying to boost the morale of his troops."
A soldier died on Thanksgiving from a gunshot wound inside the heavily fortified U.S. base in Ramadi, 60 miles west of Baghdad. Military officials have refused to describe the circumstances of the shooting.
Another soldier died Friday when four mortar shells pounded a 101st Airborne Division base in Mosul. Iraqi insurgents have stepped up attacks in previously calm Mosul in recent weeks.
U.S. soldiers in Ramadi shot a 7-year-old Iraqi child in the foot after the child pointed an AK-47 automatic rifle at them, the U.S. military said.
And a U.S. soldier was seriously wounded after a roadside bomb struck a convoy he was traveling in near the town of Samarra, about 75 miles north of Baghdad, said Lt. Col. William MacDonald, spokesman for the 4th Infantry Division.
Two other U.S. soldiers were injured when their tank struck a land mine near the Syrian border, the military said.
The military also said it had captured one of Saddam's former bodyguards, identified as Brig. Gen. Khalid Arak Hatimy. The statement said Hatimy had been inciting the uprising west of Baghdad and providing money and weapons to guerrillas.
More than 60 U.S. troops have been killed in hostile action in November, more than any other month since Bush declared the end of major combat May 1. Since operations began, nearly 300 U.S. service members have died from hostile action.