The source told CNN that investigators believe the letter to be authentic.
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"The [Gulf Cartel] apologizes to the society of Matamoros, the relatives of Ms. Areli, and the affected American people and families," reads the handwritten letter, referring to a Mexican woman who was also killed in the shootout. Two other American tourists survived the kidnapping.
In one of the photos posted online, five men can be seen lying face down and restrained on the pavement with their shirts pulled over their faces. Uniformed authorities are seen standing over them.
"The Gulf Cartel, Scorpion Group, strongly condemns the events of last Friday," the letter continues, referring to a division of the cartel. "For this reason, we decided to hand over those directly involved and responsible for the acts, who at all times acted under their own determination and indiscipline and against the rules in which the [Gulf Cartel] always operates."
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CNN cannot confirm the authenticity of the photos and has asked Mexican and US authorities for comment.
It is common for Mexican cartels, especially in the northeast of the country, to release messages to the authorities or rival groups in the aftermath of high-profile incidents, according to Guadalupe Correa-Cabrera, a professor at George Mason University who studies the cartels.
The official who confirmed the apparent legitimacy of the letter said Mexican and US law enforcement officials investigating the kidnapping strongly doubt the sincerity of the group's apology. But they suspect the apology was issued after the attack brought considerable public attention and scrutiny onto the actions of the cartel.
The development comes after a local leader of the Gulf Cartel, wanted for past kidnappings, was arrested by Mexican authorities in Reynosa, according to a US official briefed on the apprehension.
Any connection to last week's armed kidnapping of four Americans was unclear. But, as CNN has reported, the official believes members of the Gulf Cartel attacked the Americans in Matamoros in a case of mistaken identity.
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The local cartel leader, Ernesto Sanchez-Rivera, is also known to have ties to the Jalisco New Generation Cartel, the source added.
CNN has reached out to the local prosecutor for more information on the apprehension but has not yet received a response.
Meanwhile, the bodies of two Americans killed in the kidnapping are expected to be returned to the US on Thursday, a source from the Mexico Attorney General's Office tells CNN, after two survivors of the attack returned to the US for treatment at a hospital.
The remains of Shaeed Woodard and Zindell Brown likely will be transported to a funeral home in Brownsville, Texas, a US official familiar with the investigation said. The repatriation would come two days after the bodies were discovered alongside their two surviving friends in a house around the Mexican city of Matamoros.
Autopsies were completed Wednesday morning in Mexico, an official from the Tamaulipas Prosecutor's Office told CNN, though Mexican authorities have not released causes of death. Second autopsies will be performed in the US, the US official said.
CNN has reached out to the US State Department about the repatriation of remains.
The deceased were part of a group of four friends from South Carolina who had driven Friday into Matamoros so one of them, Latavia Washington McGee, could undergo a medical procedure, two family members told CNN. But their trip was violently interrupted when unidentified gunmen fired on their van, then loaded the Americans into a vehicle and drove them away, the FBI said.
An innocent Mexican bystander was also killed by a stray bullet almost a block and a half from where the Americans were kidnapped, according to Tamaulipas Gov. Américo Villarreal.
James Woodard, Shaeed Woodard's father, said it was difficult to see the video of his son's abduction on television.
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"That was so hard for me to see those videos and see him dragged and thrown on the back of the vehicle," the elder Woodard said on Thursday, which would have been his son's 34th birthday. "He was a baby and for him to be taken from me like that was very hurtful. My family is hurt real bad because he was so lovable. He had the biggest heart."
Survivor Eric Williams was shot three times in the legs, his wife Michele Williams told CNN. When he and McGee were discovered alive Tuesday, Williams was taken to a hospital in Texas for surgery, she said.
Washington McGee was also taken to the hospital, her mother, Barbara Burgess, told CNN, though Mexican authorities said she was uninjured.
"She watched them die," Burgess said, recounting what Washington McGee told her about the kidnapping. "They were driving through and a van came up and hit them, and that's when they started shooting at the car, shooting inside the van. ... She said the others tried to run and they got shot at the same time."
Washington McGee and Brown are cousins who were raised together as closely as siblings, Burgess said.
"He was a good person, and I miss him," Burgess said of Brown. "I loved him. (There's) nothing I wouldn't do for him."
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