A Border Patrol agent was killed and his partner seriously injured on Sunday morning in an attack in rural West Texas while they were on patrol, according to the federal authorities and Senator Ted Cruz of Texas.

The United States Customs and Border Protection provided few details about what happened but said the agents were “responding to activity” near Interstate 10 in Culberson County, Tex., about 90 miles east of El Paso, when the episode occurred. The agent who survived reported they had been hurt and needed help, the agency said in a statement.

Other agents responded and took them to a hospital, where one of the agents, Rogelio Martinez, 36, died. His partner, whose name was not released, was in serious condition in a hospital, the authorities said.

While officials did not specify what took place, Mr. Cruz, a Republican, said in a statement on Sunday afternoon that the agents had been attacked. “This is a stark reminder of the ongoing threat that an unsecure border poses to the safety of our communities and those charged with defending them,” the statement said.