Garza said Ortiz wasn't immediately identified as the suspect in the woman's kidnapping and the previous deaths.
An arrest affidavit states that Ortiz provided officers with details about picking up a woman he identified as Melissa Ramirez on September 3. She alerted police who caught up with Ortiz at about 2 a.m. Saturday morning. Ortiz fled before troopers arrived and killed two more people, investigators explained.
"It's interesting that he would be observing and watching as law enforcement was looking for the killer, that he would be reporting to work every day like normal", Alaniz said. He's also accused of injuring a fifth woman who escaped.
"It's hard to get into the mind of a killer", Webb County-Zapata County District Attorney Isidro Alaniz said Monday.
Ortiz is charged with four counts of murder, aggravated assault with a deadly weapon and unlawful restraint.
"I believe that it's just kind of like a small piece of it", said Alberto Luera, a second cousin of 42-year-old Claudine Anne Luera, who was discovered shot on a rural roadside Thursday.
Ortiz told police he shot the woman once in the head.
"He picked [the fifth woman] up, she went willingly with him and then while she was with him things started to get risky for her and when she tried to escape from him at a gas station that's when she ran into a trooper", Alaniz said.
Fear of additional victims is particularly haunting for sex workers, including Christa Daring, executive director of Sex Workers Outreach Project-USA. All of them died between September 3 and September 15 and their bodies were found within miles of each other.
The Border Patrol said there was nothing in Ortiz's background suggesting he was capable of such crimes.
He is the second Border Patrol agent in Laredo to be arrested on a murder charge this year after Ronald Anthony Burgos-Aviles was accused of killing a woman with whom he was romantically involved and her 1-year-old child.
On Saturday, authorities released the name of a third victim - Humberto Ortiz, 28, whom authorities referred to as a transgender woman.
Chief Deputy Garza said Ortiz "mentioned the dislike for the community. the victims represented" - presumably a reference to a comment made under police questioning.
Ortiz worked as an intel supervisor for U.S. Customs and Border Protection. "At said location, a single spent casing was discovered near the body". Jail records don't list an attorney for him. U.S. Customs and Border Protection issued a statement saying that it was fully cooperating with the investigation.
Authorities said he had one minor allegation on his record but nothing else that indicated worrisome behavior.
Garza tried to assure the public that authorities feel they have the right suspect in custody. Ortiz asked for the handcuffs to come off, and the circumstances behind the killings began to trickle out, the district attorney said.