A Mexican official says the search for an American tourist believed to have been shot while crossing a border lake is suspended indefinitely.

"There is a recess," Ruben Dario Rios Lopez, a spokesman for the state attorney general's office in Tamaulipas, told The Monitor of McAllen in a copyright story in its online edition Thursday. "We are going to look into new strategies between both U.S. and Mexican authorities in order to see what we can do, because up to now we have not been able to recover the body of this person."

Tiffany Hartley says that on Sept. 30, she and her husband, David, were returning to the United States from Mexico where they went to photograph a historic, half-submerged church.

They were crossing Falcon Lake on Jet Skis when pirates who patrol the Mexican half of the lake opened fire, shooting David in the back of the head. Tiffany Hartley says she barely escaped with her life after vain attempts to save her husband while men on three speedboats pursued them, firing their guns.

But the death may have been a case of "mistaken identity," according to a global intelligence firm.

A report released Wednesday by the Texas-based intelligence firm, STRATFOR, says members of the Zeta drug cartel may have targeted David Hartley because they mistook him as a spy for Gulf cartel, a rival drug trafficking group.

Mexican identified two suspects -- Mexicans Pedro Saldiva Farrias and his brother, Jose Manuel Saldiva Farrias  -- both believed to be members of the Zeta drug cartel from Nueva Ciudad Guerrero.

The report, obtained by FoxNews.com, says it's likely that the Hartleys were misidentified as members of the rival cartel. 

The couple used a vehicle with a Mexican license plate to transport their Jet Skis to the U.S. side of the lake. The church they intended to see, Old Guerrero, is a spot notorious for cartel members to conduct "surveillance and countersurveillance operations," the report said. 

The STRATFOR report says that Hartley's body was likely destroyed after it was determined he was American to "prevent a backlash" from the U.S. government.

Leaders of the Zeta drug cartel are reportedly angered that its lower-level operatives carried out an unauthorized shooting on Hartley, according to the San Antonio Express-New.

"The cartel boss — Miguel Treviño — is highly upset over the fact that these individuals shot and killed Mr. Hartley and it's our understanding that the cartel boss is hunting for the killers of Mr. Hartley so he can take care of them himself,” Fred Burton, the firm's vice president of intelligence, told the newspaper.

The STRATFOR report also claims that the beheading Tuesday of Rolando Armando Flores Villegas, the lead Mexican investigator in the case, was a "stern signal to both the United States and Mexico that no body will be produced and to leave the situation alone."

The U.S. government, meanwhile, said Thursday that it is doing everything possible to help Hartley's family. 

Secretary of State Hillary Clinton told ABC's "Good Morning America" on Thursday that "the beheaded body of the brave Mexican investigator that just showed up shows what we're dealing with."

The Associated Press contributed to this report.