Also Sunday, the United States continued its prosecution of top members of Saddam Hussein's regime, with reports of the capture of two top officials.
The Marines are to take up new positions in the south, reducing the number of soldiers in the Iraqi capital, military officials said. The Army's 3rd Infantry, 4th Armored and 101st Airborne Divisions are to share security duties with Iraqi police officers.
As part of the transition, the Marines also turned over the Civil-Military Operations Center at Baghdad's Palestine Hotel, U.S. Central Command said.
The center directed civil-military operations in key functional areas, such as electricity, law enforcement, water and sanitation, and medical care.
Speaking after attending Easter Sunday services at 4th Infantry Division Memorial Chapel at Fort Hood, Texas, President George W. Bush told assembled reporters the war would be over "when (U.S. Central Command head Gen.) Tommy Franks says it's complete."
In response to a question about the status of the Iraqi leader, he later said: "Saddam Hussein is no longer in power. That's for certain. He was in power, and now he is not. And, therefore, the Iraqi people's lives will be much better off. But other than that ... we'll just have to see."
He added, "If (Saddam) is alive, I would suggest he not pop his head up."
Bush also said there were "some positive signs" in the issue of Syria, which the United States has accused of harboring fleeing Iraqi officials. "They're getting the message that they should not harbor Baath Party officials, high ranking Iraqi officials. A lot of other countries have also sent that message," Bush said.
U.S. Central Command in Qatar Sunday acknowledged reports that the opposition Iraqi National Congress has custody of Saddam's last living son-in-law, Jamal Nustafa Abdullah Sultan al-Tikriti. INC told media outlets al-Tikriti, No. 40 on Centcom's "Iraqi Top 55" list, had surrendered to the group and soon will be handed over to Coalition forces in Baghdad, but Centcom reported it did not have confirmation on the reports. Al-Tikriti is the "9 of clubs" on Centcom's deck of wanted Iraqi officials.
Also Sunday, Centcom confirmed the capture of Iraq's minister of higher education and scientific research, Abd al-Khaliq Abd al-Gafar, No. 54 on the top 55 list.
Seven U.S. POWs returned from Iraq via Germany to flag-waving welcomes at Fort Bliss and Fort Hood, Texas.
"My fellow Americans, I'd like to start off and say how overwhelmed I am with the tremendous support I got from you all. I'm speechless," Chief Warrant Officer David Williams, one of the former POWs, told the Fort Bliss crowd.
"It feels really good to be home. Let's keep praying for those soldiers who are still fighting. God bless America," he said.
The POWs had been shown on Iraqi TV, helpless as they were being interrogated after their March 23 capture. For most of the three weeks of their captivity they remained out of sight, getting kicked and beaten but, they said, not tortured.
"Thank you for your outstanding support, this means the world to all of us ... God bless America. This is why we live in a great country," said Joseph Hudson, one of the five freed members of the 507th Maintenance Company from Fort Bliss.
The two others -- Williams and Ronald Young -- both Apache helicopter pilots of the 1st Cavalry Division, flew on to their base in Fort Hood.
The United States, meanwhile, expects long-term military ties in Iraq, one that would grant the Pentagon access to as many as four bases there, The New York Times reported Sunday.
One of the bases would be at the international airport just outside Baghdad, according to Bush administration officials quoted in the report.
The others would be at Tallil, near An Nasiriyah in the south; at an isolated airstrip called H-1 in the western desert, along an old oil pipeline that runs to Jordan; and at the Bashur air field in the Kurdish north.
"There will be some kind of a long-term defense relationship with a new Iraq, similar to Afghanistan," said one senior administration official.
"The scope of that has yet to be defined -- whether it will be full-up operational bases, smaller forward operating bases or just plain access."
The military is already using these bases to support operations against the remnants of the old government, to deliver supplies and relief aid and for reconnaissance patrols.
Col. John Dobbins, commander of Tallil Forward Air Base, said the Air Force plan envisioned "probably two bases that will stay in Iraq for an amount of time."
"That amount of time, obviously, is an unknown," he told the Times.
But as the invasion force withdraws in the months ahead and turns over control to a new Iraqi government, Pentagon officials expect to gain access to the bases in the event of some future crisis, according to the report.