For the first time since its defeat by U.S.-led coalition forces in 2003, Iraq is in command of its own armed forces.

"From today forward, the Iraqi military responsibilities will be increasingly conceived and led by Iraqis," top U.S. commander in Iraq Gen. George Casey said Thursday, after signing over command of Iraq's military to the government of Prime Minister Nouri al-Miliki.

Al-Maliki now has complete control over the country's small navy and air force, and of the 8th Iraqi Army Division, based in the south.

"The Iraqi Army today is rebuilt again away from sectarian violence," al-Maliki said at the ceremony.

CountryWatch: Iraq

On Wednesday, U.S. military spokesman Maj. Gen. William Caldwell described the transfer as "a huge, significant event" that was "gigantic" in its significance.

Handing over control of the country's security to Iraqi forces is vital to any eventual drawdown of U.S. forces. After disbanding the remaining Iraqi army following the U.S.-led invasion in 2003, coalition forces have been training the new Iraqi military.

It is unclear, however, exactly how quickly Iraqi forces will be prepared to take over their own security.

"It's the prime minister's decision how rapidly he wants to move along with assuming control," Caldwell said Wednesday. "They can move as rapidly thereafter as they want. I know, conceptually, they've talked about perhaps two divisions a month."

Iraqi police, meanwhile, once again were the target of attacks Thursday.

A suicide car bomb targeting a police patrol outside a gas station near the Elouya Hospital in central Baghdad killed 10 people, including four policemen, and wounded 21, police said.

Another suicide car bombing in Taiyran Square in the center of the city killed three policemen and wounded 15, the prime minister's office said. Police initially reported two civilians and two policemen were killed.

Two suicide car bombs exploded near al-Nidaa Mosque in northern Baghdad, the prime minister's office said. Nobody was hurt in the first, but the second killed three civilians and wounded 12.

Another suicide car bomb in Taiyran Square in the center of the city killed two civilians and two police special forces members, and wounded 13 people, police said.

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In western Baghdad, a roadside bombing in Qahtan Square near Yarmouk hospital wounded four people, including a policeman, Mahmoud said. Elsewhere, in the upscale district of Mansour, a roadside bomb explosion killed a man and injured his daughter and another person, police said.

The U.S. military released details Thursday on the deaths of two American soldiers.

Both died on Wednesday, the military said in separate statements. One soldier, assigned to 1st Brigade, 1st Armored Division, died in the restive Anbar province west of Baghdad "due to injuries sustained from enemy action."

A second soldier, from the 3rd Brigade Combat Team, 25th Infantry Division, was killed while on a mission near Hawija, 150 miles north of Baghdad.

The identities of the two soldiers were not released while the military contacted their families.

The Associated Press contributed to this report.