BAGHDAD, Iraq (AP) – An al-Qaida-linked group claimed Monday that it had kidnapped two American soldiers reported missing south of Baghdad, where 8,000 Iraqi and U.S. troops were conducting a massive search.

The umbrella group, called the Mujahedeen Shura Council, said it was holding the two privates _ one from Texas and the other from Oregon _ as well as four Russian diplomats kidnapped June 3 in Baghdad. It also claimed to have killed a fifth Russian.

The message, which could not be authenticated, appeared on an Islamic Web site known for publishing messages from insurgent groups in Iraq. U.S. officials have said they were trying to confirm whether the two soldiers, who disappeared Friday evening following an insurgent attack that also killed a U.S. soldier, were kidnapped.

During the search for the missing Americans, U.S. spokesman Maj. Gen. William Caldwell also said the military killed three suspected insurgents and detained 34 others in fighting that wounded seven U.S. servicemen.

The Web posting said: “Your brothers in the military wing of the Mujahedeen Shura Council kidnapped the two American soldiers near Youssifiya.” It did not identify the soldiers.

The Defense Department identified the missing men as Pfc. Kristian Menchaca, 23, of Houston, and Pfc. Thomas L. Tucker, 25, of Madras, Ore., and the dead soldier as Spc. David J. Babineau, 25, of Springfield, Mass. They were assigned to the 1st Battalion, 502nd Infantry Regiment, 2nd Brigade, 101st Airborne Division (Air Assault), Fort Campbell, Ky.

Gunmen kidnapped the four Russian diplomats near their embassy in Baghdad’s Mansour district after firing on their car and killing an embassy employee.

“God has enabled the lions of monotheism to arrest four Russian diplomats in Iraq and kill the fifth,” said a statement from the group on the same Web site.

It condemned Russian actions in Chechnya and criticized its presence in Baghdad, saying: “The Russian government sends its diplomats to Iraq to support the crusaders’ project, led by America, and to provide international backing and legitimacy to the exhausted Iraqi government.”

The Mujahedeen Shura Council is a grouping of several insurgent forces, including al-Qaida in Iraq. Former insurgent leader Abu Musab al-Zarqawi helped create the council in January, apparently to give an Iraqi face to his movement, made up mainly of foreign fighters.

In the posting, the council taunted U.S. forces for failing to find the Americans.

“The events reconfirm the weakness of the alleged American intelligence and its going astray in Iraq,” the statement said.

“The American military has launched a campaign of raids using armor and equipment, in the region around the incident, but the army of ‘the strongest nation in the world’ retreated in defeat and disgrace,” it said.

Fighter jets, helicopters, unmanned drones, boats and dive teams are being used to find the two men, Caldwell said. He did not comment on whether they had been seized by insurgents, saying only that they were listed as “duty status and whereabouts unknown.”

Foreign Minister Hoshyar Zebari said the soldiers appeared to have been taken prisoner. “Hopefully, they will be found and released as soon as possible,” he told CNN on Sunday.

Ahmed Khalaf Falah, a farmer who said he witnessed the abduction, told The Associated Press the two soldiers had been captured by seven masked, heavily armed gunmen during the attack near Youssifiya, about 12 miles south of Baghdad. The town is in the “Triangle of Death,” a predominantly Sunni region where ambushes are frequent.

Despite the presence of more than 130,000 U.S. troops in Iraq, abductions of American service members have been rare.

Sgt. Keith M. Maupin of Batavia, Ohio, was captured April 9, 2004, when his fuel convoy was ambushed. A videotape shown on Al-Jazeera TV purported to show a captive U.S. soldier shot, but the Army ruled it was inconclusive whether it was Maupin.

On March 23, 2003, in the opening days of the war, a maintenance convoy was ambushed, and 11 U.S. troops were killed and six were captured, including Pvt. Jessica Lynch and Spc. Shoshana Johnson. Lynch was rescued April 1, 2003; the others were rescued April 13, 2003.

Menchaca’s relatives said they were hoping for his safe return.

“I was 95 percent sure he was one of them,” Menchaca’s brother, Julio Cesar Vasquez, of Houston, told AP late Sunday. “I already had an idea because he was at a checkpoint.”

Caldwell said seven other U.S. service members had been wounded during the search. He said more than 8,000 U.S. and Iraqi troops were taking part.

“While searching for our soldiers, we have engaged in a number of significant actions against the anti-Iraqi forces,” he said, adding that three insurgents had been killed and 34 taken into custody.

Insurgents also continued to defy a security crackdown in Baghdad, although violence appeared to have ebbed somewhat after several bloody attacks in recent days.

A parked car bomb struck an Iraqi army convoy near a busy Baghdad square Monday, killing five people, including four Iraqi soldiers, and wounding nine passers-by, Lt. Ahmed Muhammad Ali said. A policeman also was gunned down in western Baghdad.

U.S. and Iraqi troops also pushed into an eastern section of the western insurgent stronghold of Ramadi in a campaign to gradually bolster their presence in city neighborhoods that for months have largely been under insurgent control.

A U.S. gunship fired on suspected insurgents early in the operation, U.S. commanders said. Six men were thought to have been killed, and sporadic exchanges of gunfire echoed throughout the neighborhood in the morning. No U.S. casualties were initially reported.

Prime Minister Nouri al-Maliki, meanwhile, said Iraqi forces will take over security next month in a southern province where Japanese troops are based.

The decision, announced after al-Maliki met with Japan’s ambassador, does not necessarily mean that any U.S.-led coalition forces will be withdrawn from Muthana province.

Al-Maliki has said his national unity government plans to gradually take over security for all of Iraq’s 18 provinces within the next 18 months.

In another development, 500 detainees were released from U.S.-run detention centers in Iraq, the Justice Ministry said, part of al-Maliki’s plan to release 2,500 prisoners to promote national reconciliation.

The U.S. military also said the Central Criminal Court of Iraq has sentenced 29 insurgents to up to 15 years in prison for offenses ranging from possessing illegal weapons to membership in armed groups. Five were foreigners, including an Iranian who received six years in prison after he was caught entering the country illegally.

The court has tried 1,229 suspected insurgents and convicted 1,066, it said.

In other violence Monday:

_ A former member of Saddam Hussein’s Baath Party was gunned down as he was going to work in downtown Amarah, 180 miles southeast of Baghdad.

_ Gunmen killed a police colonel heading to work near Karbala, 50 miles south of Baghdad.

_ Gunmen trying to kill a former army major in the northern city of Mosul killed a civilian and wounded their target.

_ A sniper killed an Iraqi soldier 25 miles west of Baghdad.

_ Roadside bombs in Fallujah and Hillah killed four civilians.