She then described the suspect to the officer and provided details about his vehicle and his home, Mr. Alaniz said. He said the woman told authorities that she grew suspicious of the agent after asking him about the spate of killings.

Andrew Meehan, the assistant commissioner for public affairs at the Border Patrol, said the agency was fully cooperating with investigators in the case. He said it was the agency’s policy to not comment on details of a current investigation, but added, “criminal action by our employees is not, and will not be tolerated.”

Mr. Ortiz’s arrest came on the heels of a case in April in which authorities in Laredo arrested Ronald Anthony Burgos Aviles, also a supervisor for the Border Patrol, and charged him with killing a woman with whom he was romantically involved and her 1-year-old son.

Two years ago, a senior Border Patrol agent stationed farther north up the border in Del Rio, Tex., was taken into custody and charged with distributing child pornography and attempting to entice a minor to engage in sexual activity. Federal prosecutors said the agent, Salvador Contreras, 50, sent child-porn images to an undercover agent whom Mr. Contreras believed was the mother of 8-year-old and 14-year-old girls. He had expressed, prosecutors alleged, a desire to engage in sexual conduct with both girls and had made arrangements to do so. Mr. Contreras, who was later sentenced to serve 11 years in a federal prison, had called himself a sex addict who was just “looking for his next high,” according to prosecutors.

In another case, from 2014, a Border Patrol agent in Texas kidnapped, attacked and sexually assaulted three undocumented immigrants: a woman and two teenage girls from Honduras. The agent, Esteban Manzanares, killed himself as officers closed in on his South Texas home.

Customs and Border Protection must annually report to Congress all cases of reported sexual abuse by its employees, a requirement prompted by media reports of sexual assault allegations within the agency.

In its most recent report in 2016, the agency showed that from October 2014 to September 2015 there were 52 allegations of sexual abuse and sexual assault by Customs and Border Protection employees, including Border Patrol agents. Many of the allegations stemmed from on-duty cases involving people the employees had apprehended.