The Mujahedeen Shura Council made the claim in a 4:39 minute video posted on the Internet which included the mutilated bodies of two of the soldiers attacked June 19 near Youssifiyah southwest of Baghdad, according to a statement by the SITE Institute.
The institute released still pictures from the video showing two of the American dead, one of whom had been decapitated.
According to the institute, the statement by the insurgent group said the video was released as "revenge for our sister who was dishonored by a soldier of the same brigade."
Two sergeants are among in the March 12 alleged rape-murder and the killing her parents and a younger sister. The U.S. military released the identities of the suspects Monday.
A previously discharged soldier had been arrested in the case last month and charged with rape and murder.
According to the SITE Institute, the statement by the insurgents said that as soon as fighters heard of the rape-slaying, "they kept their anger to themselves and didn't spread the news."
"They decided to take revenge for their sister's honor," the statement said. "With Allah's help, they captured two soldiers of the same brigade as this dirty crusader."
The Mujahedeen Shura Council is an umbrella organization of several Islamic extremist groups, including al Qaeda in Iraq. It claimed responsibility for shooting down a U.S. Apache helicopter in the Youssifiyah area in April.
U.S. investigators had said there was no evidence linking the deaths of the three soldiers last month to the alleged rape-slaying.
Sgt. Paul E. Cortez, Spc. James P. Barker, Pfc. Jesse V. Spielman and Pfc. Bryan L. Howard are accused of rape and murder and several other charges as alleged participants. They could face the death penalty if convicted.
A fifth, Sgt. Anthony W. Yribe, is charged with failing to report the attack but is not alleged to have been a direct participant.
The five will face an Article 32 hearing, the military equivalent of a grand jury proceeding, to determine if they should stand trial.
They are charged with conspiring with former soldier Steven D. Green, who was arrested in the case last month in North Carolina. Green has pleaded not guilty to one count of rape and four counts of murder and is being held without bond.
CBS News correspondent David Martin reports that according to Green's arrest warrant, two of the soldiers have already confessed, saying Green took the girl's parents and younger sister into a bedroom and closed the door. Shots were fired and Green came out, saying, "I just killed them." Green and one other soldier then raped the girl before Green shot her in the head, wrapped her body in a blanked and set it on fire.
The U.S. military spokesman in Iraq, Maj. Gen. William Caldwell, declined to comment further on details about the attack, saying the investigation continues.
"But they obviously had enough information in the initial investigation to go ahead and charge those four soldiers all with alleged rape, rape, obstruction of justice, housebreaking, arson and the other offenses," he told reporters in Baghdad.
Spielman, of Chambersburg, Pa., is a 2002 graduate of Chambersburg Area Senior High School.
His mother, Nancy Hess, told WGAL-TV in Lancaster, Pa., on Monday: "I don't believe the charges and I'm still proud of him." She said her son always wanted to be a soldier.
According to an FBI affidavit filed in Green's case, he and at least two others targeted the young woman and her family for a week before the attack, which was not revealed until witnesses came forward in late June.
The soldiers drank alcohol, abandoned their checkpoint, changed clothes to avoid detection and headed to the victims' house, about 200 meters (yards) from a U.S. checkpoint in the "Triangle of Death," a Sunni Arab area south of Baghdad known for its violence, the affidavit said.
The affidavit estimated the rape victim was about 25. But a doctor at the Mahmoudiya hospital gave her age as 14. He refused to be identified for fear of reprisals.
Green is accused of raping the woman and killing her and the three other family members, including a girl estimated to be 5 years old. An official familiar with the investigation told The Associated Press that Green set fire to the rape victim's body in an apparent cover-up attempt.
Iraqi authorities identified the rape victim as Abeer Qassim Hamza. The other victims were her father, Qassim Hamza; her mother, Fikhriya Taha; and her sister, Hadeel Qassim Hamza.
The March 12 attack was among the worst in a series of cases of U.S. troops accused of killing and abusing Iraqi civilians.
U.S. officials are concerned the case will strain relations with Iraq's new government and increase calls for changes in an agreement that exempts American soldiers from prosecution in Iraqi courts.
Prime Minister Nouri al-Maliki has demanded an independent investigation into the case, which comes after a series of allegations that U.S. troops killed and mistreated Iraqi civilians.