Zapata, Texas (CNN) -- Despite the grisly slaying of the Mexican government's lead investigator, the search for an American reported missing in a lake straddling the border will go on, U.S. and Mexican authorities vowed Wednesday.
"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."
But their determination has gotten them no closer to finding the body of David Hartley, who was reported to have been shot during a September 30 boating trip by gunmen investigators believe are linked to a Mexican drug gang.
"Our investigators are out there right now. A body has still not been found," said Ruben Dario-Rios, a spokesman for the attorney general of Tamaulipas state.
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, said she and her family were praying for the Flores family.
"He was so sincere and so considerate for us, it just breaks my heart that somebody would do that to him," she told HLN's "Issues with Jane Velez-Mitchell."
Tiffany Hartley told authorities that her husband was fatally shot September 30 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.
"We just want David back," she said. "Maybe they can't provide a body, I don't know. But they can provide something of evidence, anything that would tell us where David's at.
"We just want him back. Give us that, and we'll go away."
The Tamaulipas attorney general's office gave conflicting information Monday about whether authorities were pursuing a pair of suspects in Hartley's disappearance.
While Luis Homero Uvalle, a spokesman for the office, told CNN the suspects are brothers who are "well known to this area," identifying them only as "El 27" and "El 31." But Dario-Rios, the chief spokesman for the attorney general, said Flores had not indicated to him that any suspects had been identified.
Gonzalez said the killing 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."
Mexican and U.S. authorities have been conducting separate searches and holding regular meetings, U.S. State Department spokeswoman Virginia Staab said. But because the disappearance allegedly occurred on the Mexican side of
the border, the United States cannot prosecute or make arrests in the case, Gonzalez said.
Falcon Lake is about 70 miles west of the Hartleys' home in McAllen, Texas.
CNN's Ed Lavandera and Nick Valencia contributed to this report.