In an interview with CBS television, Gen. David Petraeus, overall US commander in Iraq, noted that the number of sectarian killings had fallen off after the "surge" of an additional 30,000 US troops began in February, an effort to restore order in Baghdad and nearby areas. But the number rose in May, he acknowledged.

"What all of the commanders on the ground have said repeatedly is that this is going to get harder before it gets easier," he said in the interview Monday.

Interior Ministry spokesman Maj. Gen. Abdul-Karim Khalaf said Tuesday that civilian casualties were down 34 percent in May, compared with April, although he refused to provide figures.

Figures compiled by The Associated Press showed that at least 2,155 Iraqis were killed last month, making it the third-deadliest month for Iraqis since the AP began tracking civilian casualties in April 2005. Some Interior Ministry officials put the figure at 2,123 based on police reports. The officials spoke on condition of anonymity because they were not authorized to release the information.

Khalaf insisted those figures were exaggerated. The Iraqi government has not released its own figures for months, saying they could be used to portray the security situation negatively.

Suicide bombings continue to regularly claim scores of victims in Iraq's violence, principally aimed at Shiite targets and blamed on Sunni extremists of the group al-Qaida in Iraq. But female bombers remain relatively rare.

Khalaf said a woman clad in a black abaya, the traditional Islamic cloak, approached a group of police recruits in east Baghdad's Canal district about 10 a.m. Tuesday.

"She didn't obey the guards' orders to stop and they shot her and she immediately blew up," Khalaf told the AP.

A police officer witness, who asked anonymity as he was not authorized to talk to the media, said three police recruits were lightly injured.

In early afternoon, a suicide bomber blew up his car at a police checkpoint in the al-Sofiyah area of eastern Ramadi city, 70 miles west of Baghdad, said an intelligence officer at the Anbar Salvation Center. He said the blast killed six policemen and wounded three.

The officer spoke on condition of anonymity. The center is headquarters for a Sunni tribal alliance in Anbar province opposed to the extremist group al-Qaida in Iraq.

In other violence, a Shiite Muslim cleric affiliated with the anti-American Shiite leader Muqtada al-Sadr was shot and killed as his drove his automobile in Jibala, a town 40 miles south of Baghdad, according to a police officer who spoke on condition of anonymity since he wasn't authorized to speak with the media.

Later in the morning, outside an Iraqi army headquarters in Anah, about 100 miles northwest of Baghdad, an army Humvee leaving the base came under rocket-propelled grenade fire that set it ablaze and killed all the soldiers inside, an army officer reported, speaking on condition of anonymity since he was not authorized to speak with the media.

The number of dead was not immediately reported.

The three US soldiers were abducted as they were participating in an operation to watch for insurgents placing roadside bombs on a dangerous road near Mahmoudiya, about 20 miles south of Baghdad. The militants breached the concertina wire surrounding the stationary outpost composed of two Humvees, killing four other American troops and an Iraqi.

A body found in the Euphrates River on May 23, 11 days after the attack, was identified by the US military as Pfc. Joseph Anzack Jr., 20, of Torrance, Calif.

Spc. Alex R. Jimenez, 25, of Lawrence, Mass., and of Pvt. Byron W. Fouty, 19, of Waterford, Mich., remain missing.

Gen. David Petraeus, the top US commander in Iraq, meanwhile, said it was too early to judge whether the US counterinsurgency push in Baghdad, which required the addition of about 30,000 extra US troops, is working. "We haven't even started the surge, the full surge, yet so I'll answer that in September," when he is scheduled to report to Washington on the operation, he said.

"In about two weeks or so we'll have all of the forces for the surge, all the combat forces, on the ground and you're going to see the launch of a number of different operations in a number of areas to go after al-Qaida and other extremist elements," Petraeus said in an interview aired Tuesday on CBS' "The Early Show."

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