BAGHDAD (AP) – Alert guards gunned down a black-clad woman at a police recruiting station Tuesday, a would-be suicide bomber who then exploded before their eyes. But another bomber succeeded, detonating a car bomb that killed eight people in a market in the volatile Anbar province.

The American commander here acknowledged sectarian violence was on the rise.

Meanwhile, the American command insisted it would continue the search for two abducted American soldiers despite the release of a video Monday by insurgents linked to Al Qaeda claiming they had killed the two, along with a third missing soldier whose body was found previously.

The command’s attitude was reflected in the field.

“It really doesn’t change a thing,” said Captain Aaron Bright, a 10th Mountain Division company commander whose men have spent many days on the search since the soldiers were seized in an ambush south of Baghdad on May 12. Four other American soldiers and an Iraqi were killed in that attack.

“We’re still going to continue our search and we’re never going to stop until they’re found. We’ll continue to assume they’re alive,” Captain Bright said in an e-mail to The Associated Press.

The insurgent video displayed the two missing soldiers’ identification cards. “The Americans sent 4,000 soldiers looking for them,” an unidentified voice said. “They were alive and then dead.” It offered no proof.

Among the attacks Tuesday, gunmen assassinated a local leader of Muqtada al-Sadr’s radical Shiite Muslim faction south of Baghdad, and to the north insurgents ambushed an Iraqi army vehicle, killing an undetermined number of soldiers.

As the sun rose, reports also began filtering in of headless corpses and other bodies found dumped around Iraq, many presumed victims of the relentless Shiite-against-Sunni bloodshed.

In an interview with CBS television, General David Petraeus, overall American commander in Iraq, noted that the number of sectarian killings had fallen off after the “surge” of an additional 30,000 U.S. 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,” Mr. 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.

A short time later, in Amiriyah, a town on the outskirts of Fallujah, a car bomb exploded in a market, killing eight people, said Marine Major Jeff Pool, an American military spokesman for the area.

Major Pool disputed another, earlier report saying a suicide bomber blew up his car at a police checkpoint in eastern Ramadi city, 70 miles west of Baghdad, killing six policemen and wounding three others.

That report came from an office of the Anbar Salvation Council, a Sunni tribal alliance in Anbar province opposed to the extremist group Al Qaeda in Iraq. Major Pool said there was no such attack Tuesday in Ramadi, an area touted by the American command as a model for others, because violence has been on the decline.

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 American 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 U.S. military as Private first class Joseph Anzack Jr., 20, of Torrance, Calif.

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

General Petraeus, meanwhile, said it was too early to judge whether the American counterinsurgency push in Baghdad, which required the addition of about 30,000 extra American 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 Qaeda and other extremist elements,” General Petraeus said in an interview aired Tuesday on CBS’ “The Early Show.”