BAGHDAD, Iraq (CNN) -- An al Qaeda-affiliated group on Monday claimed it kidnapped two U.S. soldiers south of Baghdad, although the captives were not named.

The group -- Mujahedeen Shura Council -- made the unverified claim in a statement posted on a Web site. It did not post images or video of the soldiers as it has in the past.

The statement said, "the strongest army in the world is turned around, ashamed of their failure [to find the soldiers] and we will give you more information on the incident in the following days."

On Sunday night, the Army identified two soldiers who went missing in the area Friday as Pfc. Thomas Lowell Tucker, 25, of Madras, Oregon, and Pfc. Kristian Menchaca, 23, of Houston, Texas.

A third soldier, Spc. David J. Babineau, 25, of Springfield, Massachusetts, was killed in the attack.

The group also said it is holding four Russian diplomats hostage and demanded Moscow withdraw troops from Chechnya, Russia, and "release all our brothers and sisters" from prison within 48 hours.

Four diplomats have been missing since gunmen attacked a Russian Embassy car on June 3. A fifth diplomat died in the ambush.

Massive sweep

U.S. and Iraqi forces were sweeping the area near Yusufiya where the two soldiers disappeared after an attack on a U.S. military checkpoint, about 30 miles (48 miles) southwest of Baghdad.

The U.S. military has been using "all available assets," including some 8,000 American and Iraqi troops, an Army spokesman said Monday.

"We will never stop looking for our service members until their status is definitively determined," said Maj. Gen. William Caldwell.

Caldwell said troops are using unmanned aerial vehicles, helicopters, boats and dive teams in the search.

"We are using all available assets --coalition and Iraqi -- to find our soldiers, and [we] will not stop looking until we find them," Caldwell said.

Seven U.S. soldiers have been wounded during the search operations, he said, and three insurgents have been killed. Another 34 suspected insurgents have been detained, he added.

In March 2003, Army Spc. Shoshana Johnson, a U.S. Army cook, was taken captive with five other soldiers after their unit was ambushed in Iraq. U.S. Marines freed them three weeks later.

"The most I can say is pray and always have hope," Johnson said Monday. "My parents went through 22 days of just not knowing what was happening and their faith is what kept them going and is what kept me going also."

The three soldiers in Friday's attack were assigned to the 1st Battalion, 502nd Infantry Regiment, 2nd Brigade, 101st Airborne Division (Air Assault) out of Fort Campbell, Kentucky, the military said.

The Defense Department waited until late Sunday to release the soldiers' names so that families could be notified.

A former mayor of Tucker's hometown, Rick Allen, told The Associated Press that he knew the soldier as strong, street smart and mechanically inclined.

"He's a tough kid. Hopefully he's got the inner strength to make it through this ordeal," said Allen, whom Tucker worked for at a gas station while in high school, according to the AP.

Menchaca's relatives said they were hoping for his safe return after learning that he was missing, the AP reported. "I'm a little bit nervous, and I cannot sleep. I worry about him, " Menchaca's mother, Maria Vasquez, told AP.

Coalition forces on Sunday expanded the search for the soldiers, who were last seen at a checkpoint near Yusufiya in an area of northern Babil province called the "Triangle of Death." Insurgents have been known to hit checkpoints there with small-arms fire.

A U.S. military official said one vehicle was found abandoned at the scene, with blood in the back and boot prints nearby on the ground.

Other troops who were near the attack reported hearing an explosion and small-arms fire and called for a quick-reaction force after they were unable to contact the neighboring checkpoint. The quick-reaction force found one soldier dead and two unaccounted for, a military spokesman said.

The New York Times reported Sunday that witnesses saw the two soldiers led to two cars by masked insurgents.

"The gunmen took them and drove away," Hassan Abdul Hadi, a farmer who grows dates and apples near the checkpoint, told the newspaper.

According to the Times, the checkpoint first came under fire from insurgents hiding in nearby fruit groves. When soldiers in two Humvees took off in pursuit of the attackers, the checkpoint came under attack from another direction by another group of insurgents, the Times reported.

Iraqi Foreign Minister Hoshyar Zebari said Iraqi troops and police were assisting in the search.

"We hope they will be found and join their units safely, but these incidents happen," he told CNN's "Late Edition With Wolf Blitzer" on Sunday. "It's a state of conflict, of confrontation, so hopefully that they would be found and released as soon as possible."

The military is continuing to search for Sgt. Keith Matthew Maupin, missing since an April 2004 attack on a U.S. convoy near Baghdad International Airport.

The Arabic-language network Al-Jazeera broadcast a videotape on April 16, 2004, showing Maupin, then 20, held hostage by Iraqi insurgents.

On June 28 of that year, Al-Jazeera said it had received a statement and videotape from militants who claimed to have killed Maupin, but U.S. officials were unable to identify the man as Maupin. In April 2005, the Army said it was maintaining Maupin's status as "missing-captured."