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Search Suspended After Decapitation

Tiffany Hartley, right, and family members, take part in a news conference with Zapata County sheriff Sigifredo Gonzalez, Jr., left, Wednesday, Oct. 6, 2010 in Zapata, Texas. Hartman husband, David, was shot by Mexican pirates on Falcon Lake last week as they were returning to the United States on Jet Skis.(AP Photo/Eric Gay)

Tiffany Hartley, right, and family members, take part in a news conference with Zapata County sheriff Sigifredo Gonzalez, Jr., left, Wednesday, Oct. 6, 2010 in Zapata, Texas. Hartman husband, David, was shot by Mexican pirates on Falcon Lake last week as they were returning to the United States on Jet Skis.(AP Photo/Eric Gay)

The murder mystery at Falcon Lake continued Thursday even as authorities suspended the search for the American tourist believed to have been shot while crossing the border lake.

Tamaulipas state attorney general spokesman Rubén Dario Rios López told the McAllen newspaper, The Monitor, that the search for David Michael Hartly was temporarily called off so that law enforcement can look into new strategies.

He said authorities hope to be able to resume the search for Hartley "in a few days."

Hartley's wife, Tiffany, says they were on their way back to the U.S. from photographing a historic Mexican church when pirates in boats opened fire on them, shooting her husband. She says she tried to help her husband but had to flee because they kept shooting.

The couple was working in Reynosa, a Mexican border town rife with drug violence, when Hartley's company moved them to McAllen, Texas, just across the Rio Grande, for safety.

They decided to take Jet Skis across Falcon Lake, which is divided by the border, to photograph a historic church. They were on their way home when pirates opened fire, killing David Hartley, according to his wife.

Just days later, a student from the University of Texas-Brownsville was shot and killed in Mexico. Jonathan William Torres, 19, was one of two people killed when his bus was hijacked in Matamoros, across the border from Brownsville.

David Hartley's father, Dennis, said his son was not aware of any violence on the lake.

"My son is a history buff. He wanted to get a picture of that church,” he said. “Not hearing of any recent activity there, David and Tiffany decided to go there and snap some pictures."

The Mexican side of Falcon Lake, where David Hartley was last seen, is in the Mexican border state of Tamaulipas. On Tuesday, Tamaulipas Gov. Eugenio Hernández Flores invited Tiffany Hartley to go to the area prosecutor's office and file a formal complaint about the alleged slaying with his guarantee of safety, according to The Monitor.

In an interview on NBC's "Today" Wednesday, she said she would decline the invitation.

"We spent 4½ hours at their office (in the Mexican Consulate in McAllen),” Tiffany Hartley said, “and we were assured that they were gone to get the paper work to Mexico City, to the authorities there, and they were going to be taking them to Reynosa the same day."

The Associated Press contributed to this story.