Jan. 17, 2013 -- A Mexican national claims to be the man who shot and killed U.S. Border Patrol Agent Brian Terry, whose death is tied to the "Fast and Furious" gun-walking scandal.

Gustavo Cruz-Lozano, who says he killed Terry, turned himself in on Wednesday on charges related to a separate incident: threatening to kill Hidalgo County, Texas Sheriff Lupe Treviño.

But before he surrendered himself, Cruz-Lozano said in an exclusive interview with Univision News' daily news magazine show "Primer Impacto" that he murdered Terry during a firefight on Dec. 14, 2010, while the agent was on patrol near the U.S.-Mexico border in Arizona. Two AK-47 rifles found at the scene were linked to the botched Operation Fast and Furious, in which the U.S. government sought to track firearms sales to violent drug cartels. But it remains unclear whether those weapons were used to kill Terry.

Cruz-Lozano, 41, was not one of the several suspects arrested in the aftermath of Terry's slaying. But in an interview with Univision News, he insisted he is the one who pulled the trigger on Terry.

"We had a drug shipment and when they took us by surprise, people started surrounding them, and that's when we ambushed them," he told "Primer Impacto" correspondent Natalia Cruz. "When they started surrounding them and they had no time to react, I was the one, I was the one that killed him."

Until now, the identity of the trigger man in Terry's murder has been unknown. The Federal Bureau of Investigation requested to see Cruz-Lozano's interview with Univision News. Cruz-Lozano agreed to the interview, which aired on Thursday, on the condition that his face be covered.

One man has already pleaded guilty for participating in Terry's murder: Mexican national Manuel Osorio-Arellanes, the Associated Press reported in October 2012. Osorio-Arellanes faces life in prison.

When Univision News contacted the Terry family's attorney, Lincoln Combs, for a reaction to Cruz-Lozano's claims, he expressed skepticism about the possibility that Cruz-Lozano was involved in the killing since his name had not been part of the investigation thus far.

The attorney said that the alleged perpetrators of Terry's death had been previously identified by the authorities. Out of the five drug cartel members involved in the killing, two are being held in the United States (the Osorio brothers), one is in custody in Mexico (Jesus Leonel Sanchez Meza) and and two others, identified as Jesus Favela Astorga and Ivan Rosario Soto Barraza, are missing. The U.S. government has offered $25,000 for information that would lead to their capture.

Another man who purchased the two rifles found at the scene of Terry's death, Jaime Avila, Jr., was sentenced last month to nearly five years in federal prison.

The "Fast and Furious" scandal sent political shockwaves through the Obama administration. Critics called the operation irresponsible for allowing guns to enter into the hands of cartel members. Around 1,400 of the 2,000 guns purchased as part of the operation were lost and nearly 100 were used in crimes in Mexico, according to a Univision News investigation.

Dozens of Republican lawmakers called on Attorney General Eric Holder to resign, alleging that he should be held accountable for the operation, which was run out of the Bureau of Alcohol, Tobacco, Firearms and Explosives (ATF). Ultimately, the Department of Justice's inspector general issued a report that cleared Holder and placed blame on other ATF and DOJ officials.

Cruz-Lozano told Univision News that he was going to reveal his identity to FBI officials because he is tired of being a fugitive and that he hopes that by turning himself in, he could receive life in prison instead of the death penalty. He also claimed that he threatened Sheriff Treviño because he was investigating drug traffickers in the area.

"If it were in front of this man, not only would say that I am sorry but that I am willing to pay for all the crimes I committed," said Cruz-Lozano.