(CNN) Rogelio Martinez was always one to follow the rules. So when he saw an opportunity to become a US Border Patrol agent, he joined to help enforce the law, said his mother, Elvia Martinez.

Rogelio was "a very good man, a very good son," she said. He stayed in touch with her every single day on the phone.

Until this weekend.

Martinez, 36, died at a hospital Sunday morning, a day after he was found injured in a culvert in southwest Texas in what the FBI has described as a "tragic incident." Both Martinez and another Border Patrol agent suffered traumatic head injuries and other wounds such as broken bones, according to the FBI.

But the details of what happened to the agents remain unclear, and Elvia Martinez said the entire family cannot understand why her beloved son is dead.

"I loved him, and I miss him," she said.

The FBI, which is leading the investigation, has not yet said what caused the fatal injuries. Emmerson Buie Jr., the special agent in charge of the FBI's El Paso division, said on Tuesday the agency is investigating a "potential assault on a federal officer."

"If the facts support that, then we would pursue it legally," he said. "If they support that the incident was caused by something else, then we'll present that."

Several elected Texas officials have described the incident as an "attack," and President Donald Trump cited it on Twitter as a reason to build his border wall

But Culberson County Sheriff Oscar Carrillo told the Dallas Morning News the injuries may be consistent with a fall into the culvert.

"The evidence is not obvious as to what happened out there," Carrillo said.

The culvert is on the edge of the interstate. There is about a 10-foot drop to the cement bottom. On Wednesday, a strand of crime scene tape was visible in the culvert.

What we know

Martinez had been a border patrol agent since 2013, officials said. He and his partner were on patrol near Interstate 10 in the Big Bend Sector of Texas when they responded to activity, according to US Customs and Border Patrol.

Martinez's partner reported that they were both injured and needed help, according to CBP. They were found about 12 miles east of Van Horn at 11:20 p.m. on Saturday, according to the FBI.

Martinez was not shot, a CBP spokesman said. The results of his autopsy are pending, the FBI said.

The other Border Patrol agent survived but was having trouble remembering the incident, said Chris Cabrera, a spokesman for the National Border Patrol Council.

The injured agent, who joined the CBP in 2009, was released from a hospital on Wednesday, a hospital spokesman said.

Rush Carter, the special operations supervisor and public affairs officer for the Big Bend Sector of the US Border Patrol, said Martinez was not responding to a sensor but was on his regular duties, which included checking culverts off the interstate for illegal immigrants hiding.

JUST WATCHED FBI details Border Patrol agents' injuries Replay More Videos ... MUST WATCH FBI details Border Patrol agents' injuries 02:04

Carter said it was unclear whether Martinez radioed for help. There is no recorded radio traffic of him calling for backup and so it is unclear how the second officer ended up there.

Carter said it is possible Martinez did radio for help and it wasn't recorded because agents can use "direct mode" or "car to car mode" to radio only cars that are within a few miles from them.

Martinez leaves behind a son, two brothers and a fiancee, according to his obituary . He graduated from Irvin High School in El Paso in 1999 and studied graphic design in school, his mother said.

He was "always smiling," she said, and it was "hard to make him mad."

Reactions from leaders

The office of Texas Gov. Greg Abbott referred to Martinez's death as a murder and authorized a reward of up to $20,000 for information that would lead to the arrest of those responsible.

"We owe a great deal of gratitude to the brave men and women of the United States Border Patrol who serve every day to protect our homeland," Abbott said in a statement. "Cecilia and I offer our deepest condolences to the families of the agents killed and seriously injured in this attack."

Cabrera, the National Border Patrol Council spokesman, said the incident was an "ambush" and suggested that drug traffickers frequented the area.

"It was a brutal attack," said Cabrera. "This was something well thought out and planned. They executed their plan."

President Trump cited Martinez's death as a reason to follow through on his promise to build a wall between the US and Mexico.

"As you heard, we lost a Border Patrol officer just yesterday and another one was brutally beaten and badly, badly hurt," Trump said Monday. "It looks like he'll make it, but very badly hurt."

Border Patrol Officer killed at Southern Border, another badly hurt. We will seek out and bring to justice those responsible. We will, and must, build the Wall! — Donald J. Trump (@realDonaldTrump) November 20, 2017

On Sunday, Trumped tweeted, "We will seek out and bring to justice those responsible. We will, and must, build the Wall!"