Agent Rogelio Martinez and his partner were responding to unspecified "activity" while on patrol in Culberson County, which lies in the Big Bend Sector of the Texas border, when they were injured by either one or multiple suspects. Martinez's partner is in serious condition.
Conservative news outlet Breitbart reported that Border Patrol Agent, and National Border Patrol Council President Brandon Judd stated, "What we know is that Border Patrol Agent Rogilio Martinez appears to have been ambushed by a group of illegal aliens whom he was tracking", Judd said.
Texas is offering a $20,000 reward for information that leads to the arrest and conviction of the person or people who killed a US border agent and injured another.
Customs and Border Patrol spokesman Carlos Diaz declined to describe the incident in detail, saying the FBI is investigating.
Details on the circumstances leading up to their injuries and Martinez's death were not immediately available.
Trump says the wall is necessary because "it's rough territory" down there and a lot of things are happening along the border, including drug trafficking. His partner was also injured, and was taken to the hospital where he was in serious condition.
Texas Sen. Ted Cruz said the attack was "a stark reminder of the ongoing threat that an unsecure border poses to the safety of our communities and those charged with defending them". "We will, and must, build the Wall!"
Authorities were scouring West Texas on Monday for those behind an apparent attack that killed one USA border agent and injured another. 'Our resources must be increased to prevent these attacks in the future'.
Cruz said in a statement the nation is grateful 'for the courage and sacrifice of our border agents'.
Spokesman Douglas Mosier says Martinez was 36 years old and from El Paso.
They were attacked with rocks about 30 miles (48km) from the Mexico border, according to a labour union for border agents.
Federal Bureau of Investigation spokeswoman Jeanette Harper said the Federal Bureau of Investigation is still investigating and gathering facts.
That area has accounted for about one percent of more than 61,000 arrests from October of last year, until May of this year. The region's mountains and the Rio Grande make it a hard area for people to cross illegally into the USA from Mexico.