An extensive FBI investigation into the death of a border patrol agent that President Donald Trump described as a murder has found no evidence that the man was attacked.

Rogelio Martinez died from injuries sustained in November last year while responding to reports of a late-night incident near Interstate 10 in remote west Texas, about 30 miles from the border with Mexico.

Trump tweeted the next day that Martinez was “killed”, adding “we will seek out and bring to justice those responsible. We will, and must, build the Wall!”.

The president later added that Martinez’s partner, who was injured and hospitalised but survived, had been “brutally beaten”.

Two senior Texas Republicans – Governor Greg Abbott, and Senator Ted Cruz – also weighed in with statements describing the 36-year-old’s death as a murder.

But the FBI has found no sign of an attack, adding credibility to suggestions that the incident was an accident.

“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,” the bureau’s El Paso office said in a statement on Wednesday.

The FBI is offering a reward for information and said that 37 of its field offices were involved in the “top priority” investigation, which included 26 searches in Texas and New Mexico and turned up two “persons of interest” who were found not to be involved, while “several individuals” were arrested on suspicion of an unrelated immigration offence.

The release provided a detail that was not previously made public: when talking to a dispatcher by phone, the second agent “made a statement to the effect of, ‘We ran into a culvert,’ ‘I ran into a culvert,’ or ‘I think I ran into a culvert’.”

The agent later told investigators he had no memory of what occurred because he suffered head injuries.

The FBI statement follows an inconclusive autopsy report released by the El Paso county medical examiner’s office on Tuesday which said the death was caused by blunt force trauma from an undetermined cause.

Border patrol union representatives have consistently maintained that Martinez was deliberately killed, perhaps after being struck with rocks.

“Just because there’s no evidence of a scuffle doesn’t mean that it wasn’t an assault,” Brandon Judd, president of the National Border Patrol Council, told Fox News. “The only thing in my mind that makes sense is that they were attacked from behind.”

However, the local sheriff, Oscar Carrillo, told the Dallas Morning News last year that “from the beginning we were radioed to assist in the incident as an injury, not an assault.” Carrillo raised the possibility that the agents might have tumbled roughly 9ft into the culvert from the edge of the often windswept freeway, given the darkness and the risk of being sideswiped by a truck.

Trump has repeatedly seized on fatal incidents to advance the narrative that more border security and tougher immigration restrictions and enforcement are required to keep Americans safe.

He tweeted that the death of the NFL player Edwin Jackson last weekend in a suspected drunk-driving accident involving a previously deported undocumented immigrant from Guatemala was “disgraceful” and “just one of many such preventable tragedies”.

In response, the local prosecutor, a Democrat, said that attempts to politicise the crash were “ghoulish and inappropriate”.