Story highlights "We will, and must, build the Wall," Trump tweets

Agent Rogelio Martinez was killed and his partner was serious injured

(CNN) Details remain scant in what the FBI describes as a "tragic incident" that left one Border Patrol agent dead and another in serious condition.

The FBI said both men were found injured late Saturday in a culvert area in southwest Texas.

Rogelio Martinez, 36, died from his injuries at a hospital Sunday morning. His partner, who hasn't been identified, remains hospitalized in serious condition.

The two Border Patrol agents suffered traumatic head injuries and other wounds such as broken bones, according to the FBI, which is leading the investigation. The results of Martinez's autopsy are pending.

Although there hasn't been an explanation of what happened, Texas politicians -- including Gov. Greg Abbott and Sen. Ted Cruz -- have described the incident as an "attack." President Donald Trump said the injured agent had been "brutally beaten" as he called for the wall between US and Mexico.