(CNN) -- Secretary of State Hillary Clinton said Thursday the United States is "doing everything that we know how to do" to find the body of an American reported missing in a lake straddling the U.S.-Mexican border.
Clinton told ABC's "Good Morning America" that she is "sickened" by the case involving American David Hartley.
"I hope that we can [find him]," said Clinton. "I mean, the beheaded body of the brave Mexican investigator that just showed up shows what we're dealing with."
She said the United States is "supporting local law enforcement, supporting the authorities on the border, doing everything that we know to do to try to assist in helping to find the body and helping to find the perpetrators."
Clinton's comments came a day after U.S. and Mexican authorities vowed the search for Hartley would continue despite the grisly slaying of the Mexican government's lead investigator in the case.
"We continue the search on this side of the border," Zapata County, Texas, Sheriff Sigifredo Gonzalez Jr. told CNN. "We're also sending a message that we're here."
Hartley is reported to have been shot during a September 30 boating trip by gunmen investigators believe are linked to a Mexican drug gang.
The search resumed after this week's killing of state police official Rolando Armando Flores Villegas, whose severed head was delivered to the Mexican military in a suitcase Tuesday, officials said.
Tiffany Hartley, the missing man's wife, told authorities that her husband was fatally shot during a sightseeing trip the two were taking on Falcon Lake, a reservoir on the Rio Grande. Gonzalez has said the gunmen were likely pirates linked to one of the Mexican drug cartels, and Hartley has said she believes the attackers may still have her husband's body.
Meanwhile, a report issued by a Texas-based think tank suggested Thursday that David Hartley's death may have stemmed from a case of mistaken identity in the ongoing war between two Mexican drug cartels.
The Stratfor report, which cites anonymous sources, noted that David Hartley worked for an oil and gas company with operations in Reynosa, Mexico, and the couple had lived there for two years and had only moved to McAllen, Texas, within the past few months. The truck they drove to Falcon Lake on September 30 still had a license plate from Mexico's Tamaulipas state.
The couple drove their personal watercraft to the Old Guerrero area of the lake, which the report said is a "known battleground in the ongoing war in the Los Zetas and Gulf cartels." The sources told Stratfor both cartels have been known to conduct surveillance and countersurveillance operations on personal watercraft, so Zetas scouts identified them as possible Gulf spies, because of their license plate and their method and direction of travel on Falcon Lake. They were then apparently confronted by "Zetas enforcers," Stratfor said.
The sources told Stratfor the attack was unauthorized by senior Los Zetas members and "a damage control campaign is currently under way ... to identify and eliminate those who engaged the Hartleys without proper authorization." Protocol involves prompt disposition of a body to ensure no evidence can be brought against the group, the report said.
Sources said that "once Hartley was identified as an American, his body was destroyed the same day as the incident to prevent a backlash from the U.S. government against the group," Stratfor said. "With the heavy diplomatic and public pressure on both U.S. and Mexican authorities to find David Hartley's remains in the investigation, the decapitation of Flores Villegas was a stern signal to both the United States and Mexico that no body will be produced and to leave the situation alone."
The Tamaulipas attorney general's office gave conflicting information Monday about whether authorities were pursuing a pair of suspects in Hartley's disappearance.
Gonzalez said the killing of Flores was intended as "a message to Mexico to back off, for the search to stop." But while searchers returned to the 60-mile-long lake Wednesday, the sheriff said the prospects for finding Hartley's body are fading.
"We have to admit that our chances are getting slimmer and slimmer as we go along," he said. "It's hard for the family."
The State Department has said Mexican and U.S. authorities have been conducting separate searches and holding regular meetings, but because the disappearance allegedly occurred on the Mexican side of the border, the United States cannot prosecute or make arrests in the case.
Falcon Lake is about 70 miles west of the Hartleys' home in McAllen.