The United States anxiously awaits the day it can hand over control of Iraq to its people, Defense Secretary Donald H. Rumsfeld assured Iraqis on Wednesday.

"I am delighted to be able to visit Baghdad and your country and witness the liberation of your country," he said in a message taped for radio and television broadcast in the Baghdad area.

He told U.S. troops at Baghdad International Airport (search) that, "the American people are proud of you" and congratulated them on an operation well done.

Rumsfeld (search), operating out of a palace that once belonged to ousted Iraqi President Saddam Hussein, told Iraqis that coalition forces would stick around to restore order and basic services for Iraqis and help them form a new government.

The Bush administration has repeatedly said it has no interest in running the government and that it should be run by Iraqi citizens.

President Bush was expected to declare the fighting in Iraq over in an address to the American people Thursday night.

The first top Bush administration official to visit Iraq since Saddam's ouster, Rumsfeld also called on Iraqis to tell coalition solders about former Iraqi officials and foreign fighters who might still be in their neighborhoods.

"Iraq belongs to you," he said. "The coalition has no intention of owning or running Iraq."

To the troops at Baghdad International Airport, Rumsfeld said: "I have to say I'm surprised to see you guys here.

"The world was told there were no Americans here over and over and over," he added, "but I guess that's the last time we heard from that fellow," apparently referring to Iraqi Information Minister Mohammed Saeed al-Sahaf (search), who during the fighting repeatedly denied coalition troops were anywhere near Baghdad.

Al-Sahaf disappeared the day before U.S. tanks rolled into the heart of Baghdad.  News reports Wednesday indicated that he was trying to surrender to coalition troops, but was being rebuffed.

"What you have accomplished is truly remarkable," Rumsfeld told the troops. "You've rescued a nation, you've liberated a people, you've deposed a cruel dictator and you've ended his threat to free nations."

The coalition's march toward Baghdad "was possible the fastest march on a capital in modern military history," the defense secretary added.

He said the coalition should pride themselves on working to avoid civilian casualties and aim only at the enemy.

"While your adversary did everything in his power to put civilian lives at risk, you, our coalition partners, took such great care to protect the lives of innocent civilians," he said.

But the coalition's work is far from over, he said.

"There's still work to be done. The remnants of that regime need to be removed from every corner of the country," Rumsfeld stressed, adding that U.S. forces must provide security and stability to the nation before Iraqis can run their own country.

Earlier on Wednesday, the defense chief met with Jay Garner, the retired Army general serving as civilian administrator of Iraq until a new government is up and running, as well as with U.S. military commanders.

Garner told reporters Americans should be proud of the quick military victory in Iraq.

"I was planning on having the oilfields torched and facing a huge humanitarian crisis, but the oilfields were not torched and there is no humanitarian crisis," said Garner.

Lt. Gen. David McKernan, commander of the coalition land forces that took Iraq, also said operations were going extremely well.

"For every one thing that doesn't look right or smell right, there are 10 things going well," McKernan said.

Rumsfeld will visit an electricity generating plant south of Baghdad that coalition forces helped restart after the war. Garner said about half of Baghdad has electricity.

Rumsfeld and his party flew to Baghdad after a stopover in the southern city of Basra where he met with British Maj. Gen. Robin Brims, commander of the forces that gained control of Iraq's second-largest city.

"A number of human beings have been liberated and they are out from under the heel of a vicious, brutal regime," Rumsfeld said prior to his meeting with Brims. "I'm very pleased that the United States and the United Kingdom worked so well together."

Brims agreed that U.S. and British forces worked great together.

"There are exceptional capabilities that your military bring that we are very envious of," Brim said.

Rumsfeld's visit to Iraq came the day after he announced that U.S. troops in neighboring Saudi Arabia will leave that country by the end of the summer, marking a major shift in the American military presence in the Persian Gulf.

The United States will all but abandon Price Sultan air base at a remote desert base south of the Saudi capital of Riyadh.

Only about 400 U.S. troops will remain in the Muslim kingdom, most of them based near Riyadh to train Saudi forces, American officials said Tuesday.

Rumsfeld and Saudi Defense Minister Prince Sultan said the pullout is because, with the war won in Iraq, forces are no longer needed to patrol the old no-fly zone over southern Iraq.

About 100 U.S. planes now remain at the Saudi base, down from about 200 during the height of the Iraq war. All will be gone by the end of August.

Part of Rumsfeld's mission in the Persian Gulf region this week is to talk to American allies about rearranging U.S. military forces in the area after the Iraq war.

The United States also has troops in the United Arab Emirates, Qatar and Kuwait, which Rumsfeld also visited this week, as well as Bahrain and Oman.

The defense secretary has said he wants to have fewer troops in the Persian Gulf after all operations in Iraq are complete. That process could take years, however. Rumsfeld also has said the United States does not want permanent access to bases inside Iraq.

One unresolved issue confronting Washington is whether Saddam's regime actually had illegal weapons of mass destruction, as the White House insists it does.

U.S. officials said Tuesday that high-ranking Iraqis now in custody are denying that Saddam's government had any biological, chemical or nuclear weapons. The officials said they believe many of the prisoners are lying to protect themselves.

American officials are still staunch in their insistence, however, that Iraq had prohibited weapons and the means to make more. They have suggested that the weapons were well hidden or destroyed shortly before the war.

British Prime Minister Tony Blair told an interviewer Wednesday that doubters of the existence of Iraqi weapons of mass destruction would be left "eating some of their words."

Fox News' Liza Porteus and The Associated Press contributed to this report.