Authorities haven't offered an official explanation of what happened when a U.S. border agent died and another was badly injured while working over the weekend in West Texas, and a border patrol supervisor says reports they were attacked are "speculation."

Several elected officials, including President Donald Trump, have called the death of Rogelio Martinez, 36, an attack. Rush Carter, a supervisor for the U.S. Customs and Border Patrol region that includes the area where Martinez died, said all the agency can confirm is that the two "were injured while performing their regular duties" and that a joint investigation with the FBI is underway.

"We are waiting for the investigation to fully determine how those injuries happened," Carter said Monday night.

CBP issued a statement Sunday that was thin on details, saying the two agents "were responding to activity" near Interstate 10 and close to Van Horn, about 30 miles (48 kilometers) from the border with Mexico and 110 miles (175 kilometers) southeast of El Paso. A CBP spokesman said in the statement that Martinez and his partner were taken to a hospital, where Martinez died. Martinez's partner, whose name hasn't been released, was in serious condition.

Kevin McAleenan, acting commissioner of CBP, said in a letter sent to border agents on Sunday that Martinez was unconscious when agents found him with "multiple injuries" to his head and body.

Jeanette Harper, an El Paso field office spokeswoman for the FBI, which is leading the investigation, told the San Antonio Express-News on Sunday that Martinez and his partner were "not fired upon," but she didn't elaborate.

However, Chris Cabrera, a spokesman for a border patrol agents union, the National Border Patrol Council, told The Associated Press that the two agents appeared to have been struck in the head with a rock or rocks. Cabrera said agents who responded to the scene described it as "grisly" and said Martinez and his partner had "extensive injuries."

ABC News, citing unnamed sources, reported Monday that investigators are open to the possibility that the two agents may have inadvertently slipped into a ravine.

Texas Gov. Greg Abbott announced a $20,000 reward Monday for information that leads to an arrest or conviction in the case. The Republican also tweeted that "resources must be increased to prevent these attacks in the future."

Republican Sen. Ted Cruz took a similar approach in a news release: "We are grateful for the courage and sacrifice of our border agents who have dedicated their lives to keeping us safe."

Trump offered his condolences to Martinez's family and said the wall he has promised to build along the border between the U.S. and Mexico is on the agenda. Trump said the injured agent was "brutally beaten and badly, badly hurt" but "looks like he'll make it."

Authorities haven't said whether they have any suspects or whether they think smugglers or people who were in the country illegally were involved.

Border Patrol records show that the agency's Big Bend sector, which includes the area where the incident occurred, accounted for about 1 percent of the more than 61,000 apprehensions its agents made along the Southwest border between October 2016 and May 2017. The region's mountains make it a difficult area for people to cross illegally into the U.S. from Mexico.

The Border Patrol website lists 38 agents, not including Martinez, who have died since late 2003. Some were attacked while working along the border and others were killed in traffic accidents.

Martinez is the second agent to have died this year.