Six Union Pacific Railroad employees working in the area were also interviewed and 26 searches have been carried out in separate parts of Texas and New Mexico.
And President Donald Trump said the injured agent had been "brutally beaten" as he called again for the construction of a wall between the United States and Mexico.
"To date none of the more than 650 interviews completed, locations searched, or evidence collected and analyzed have produced evidence that would support the existence of a scuffle, altercation, or attack on November 18, 2017", said the release from the El Paso office of Emmerson Buie, a special agent in charge. He was allegedly disoriented and unsure of his exact location but told the dispatcher that he and Martinez had been injured. Ted Cruz and Texas Gov. Greg Abbott seized on the incident as grounds for tighter border security.
The statement came one day after El Paso's medical examiner released Martinez's autopsy, which found that he died of blunt injuries to his head, but couldn't determine the cause of death.
"Although disoriented and unsure of his location", according to the Federal Bureau of Investigation statement, Garland told a Border Patrol dispatcher something to the effect of "we ran into a culvert" or "I ran into a culvert" or "I think I ran into a culvert".
"From the beginning we were radioed to assist in the incident as an injury, not an assault", he said.
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Martinez's partner Stephen Garland, who suffered serious head injuries during the incident, told investigators he is unable to recall specific details of what happened that night, according to the Washington Post.
"This investigation has been the top priority of the El Paso FBI Field Office, and the FBI has aggressively pursued all logical leads and investigative avenues", the FBI said in a statement released Tuesday afternoon. As part of this effort, the FBI has investigated multiple theories, including whether the Border Patrol Agents were ambushed or attacked or whether their injuries were as a result of an accident or any other relevant criminal activity.
"The FBI had identified two persons of interest, but through forensic analysis both have been determined not to have had anything to do with the death of Agent Martinez and the injuries to his partner", according to the statement.
"The absence of evidence is a key factor in this case - not due to lack of effort or determination, but because evidence which would indicate the presence of other persons or the commission of a criminal act is not present", the memo reads. They have found no evidence to support that. The manner of death is undetermined.
The men, from Portales, have been indicted for "offenses involving the smuggling of an alien".
The FBI has been considering several possibilities, including an accident, an attack or an altercation between the two agents, a Department of Justice official with knowledge of the investigation said. The FBI said they'll continue to investigate and they're offering a $50,000 reward for information that helps close the case.