Mexico City, Mexico (CNN) -- Mexican authorities have bolstered their search for a missing U.S. citizen and the government rejects assertions that security forces aren't doing enough to find him, the foreign ministry said Friday.
David Michael Hartley has been missing since a reported pirate attack September 30 on a lake bisected by the U.S.-Mexico border.
Hartley's wife, Tiffany, told authorities her husband was shot and killed by pirates on Falcon Lake during a sightseeing trip. His body has yet to be found, leading to questions about the accuracy of her statements.
The ministry said the federal attorney general's office opened an investigation based on testimony Tiffany Hartley gave to Mexican authorities at the consulate in McAllen, Texas. The government also has been in close touch with several U.S. authorities.
"The search and rescue for Mr. Hartley started the day of the incident, and intensified this week with additional officers from the Army, the Federal Police, and from state and municipal forces, which cover the area where the incident reportedly took place," the ministry said.
On Thursday, Tiffany Hartley said she might take a lie detector test if people continue to doubt the veracity of her account.
If "that's what the authorities think I need to do, then that might be an option," she said when asked on CNN's "AC 360" about taking a lie detector test.
Hartley was on several CNN shows Thursday recounting what happened last week on Falcon Lake. She also talked about her feelings about people doubting her account of the alleged attack.
Hartley said on HLN's "Issues with Jane Velez-Mitchell" that "I know what I know."
"It's hard being judged and thought of that I might have done something to him," she said.
But she added, "As long as I know the truth, God knows the truth. And other than that, it almost doesn't really matter to me, because I know what happened that day."
Mexican authorities said earlier this week that they could not verify the shooting, and Hartley was asked point-blank on NBC's "Today" show Wednesday whether she had anything to do with her husband's disappearance.
Pam Hartley, David Hartley's mother, said Tuesday that any suggestion that her daughter-in-law's account was inaccurate is "insane."
Investigators have found some evidence that backs up Hartley's account, including blood on her life vest, Zapata County Sheriff Sigifredo Gonzalez Jr. said Thursday. And the incident was similar to other attacks reported by boaters on Falcon Lake, about 70 miles west of the Hartley's home in McAllen.
Gonzalez has said the gunmen are typically teenagers hired by a drug cartel in the neighboring Mexican state of Tamaulipas. Mexican authorities have said the lake is controlled on their side by "organized criminals," and the sheriff called on the Zeta cartel to turn over Hartley's remains if they have them.
"We just want a body," he said.
Tiffany Hartley said she believes the attackers took her 30-year-old husband's body after he was shot in the head and fell off the personal watercraft he was riding. She said she suspects her husband's remains are more likely to have been dragged onto land than to have been left in the lake.
"We do believe if they would just go ahead and give us David's body back, it would be done. It would be concluded. We could go on with our lives," she said.
Authorities from both nations are conducting separate searches and are coordinating and holding regular meetings, State Department spokeswoman Virginia Staab said. But because the alleged crime happened on the Mexican side of the border, the United States cannot prosecute or make arrests in the case, the sheriff said.
Tiffany Hartley, 29, told HLN that the couple set out across the lake on personal watercraft for a sightseeing trip to Guerrero Viejo, a half-submerged ghost town on the Mexican side of the lake. Though there had been warnings about previous robberies on the lake, she said they had heard of no problems for several months, "So we figured everything had kind of calmed down."
Instead, she said, they were pursued by men in three boats as they left the site's historic church.
At first, "they just waved at us like we were friendly, a very friendly wave," she said. But then, as the couple passed, she said they began chasing them and firing shots.
David Hartley was shot in the head and fell off his personal watercraft, and he was unresponsive when she turned back to try to retrieve him, his wife said. While she was trying to haul him onto her craft, their attackers pulled up alongside, she said.
"They didn't say anything to me, so I don't know what they were trying to do ... but they left," she said. "They just left me there. Thankfully they didn't shoot at me. They had a gun pointed at me."
Unable to pull her husband's body out of the water, Hartley headed back across the lake to U.S. waters. She said the gunmen fired "a few more" times on her way back.
"Once I started to get going, I just went as fast as I could and didn't look back until I couldn't see them anymore," she said.
Rolando Flores, lead investigator for the Tamaulipas state police, described the area as "a conflict zone."
The state has made headlines recently as a hotbed for drug cartel violence, and there have been at least four cases of gunmen in Mexican waters robbing or threatening boaters on Falcon Lake since April, according to the Texas Department of Public Safety.
David Hartley worked for an oil company in Reynosa, Mexico, and the couple had lived on the Mexican side of the Rio Grande before moving back to the United States earlier this year, family friends said.
His aunt, Alice Harrod, told HLN's "Prime News" the family had concerns about their safety in the area, "and we were all thrilled to hear that they were moving back to Colorado," where they grew up.
"We're all very devastated. It's hard to even believe something like this could happen. We're hanging in there, but it's very, very difficult for the whole family," Harrod said.
According to Rep. Henry Cuellar, D-Texas, 60 Mexican personnel, three boats and a helicopter have taken part in the search.
Investigators resumed their work Thursday despite threats to their lives, and Cuellar suggested that the Mexican navy might need to be called in to help.
Despite the dangers on the Mexican side of the lake, Texas officials on Thursday said that the U.S. side of the body of water remains safe.
"It is just as safe now as any other time. However, there is a threat," said Rep. Ruben Hinojosa, D-Texas.
CNN's Justine Redman, Nick Valencia, Dave Alsup and Matt Smith contributed to this report.