Ortiz, Chapa said, was picked up in the early hours along Interstate 35 in Laredo.
Texas authorities charged a US Border Patrol supervisor with murder following what they called a two-week serial killing spree that left four female sex workers dead and ended when a fifth woman escaped at a gas station and found help. He said all the women worked as prostitutes and investigators were trying to find a motive for the killings.
Mr Ortiz fled but was arrested in a hotel parking lot in the city of Laredo.
Juan David Ortiz, 35, faces five felony charges, according to Webb County District Attorney Isidro R. "Chilo" Alaniz.
It is unclear what evidence suggests that Ortiz is the killer of all of the women but authorities have noted similarities in each crime. Chapa said investigators are not ruling out the possibility of more victims.
Authorities didn't disclose the victims' names or nationalities but said they may have been prostitutes.
Alaniz said officials will be looking at "potentially four charges of murder and aggravated kidnapping".
Border Patrol agents are great men and women who work hard to keep us safe, and we thank them for their work.
Sheriff Cuellar told reporters that Agent Ortiz is a 10-year veteran supervisor of the Border Patrol.
"While it is CBP policy to not comment on the details of an ongoing investigation, criminal action by our employees is not, and will not be tolerated", his statement read.
His statement added: "Our sincerest condolences go out to the victims' family and friends".
He said investigators had "very strong evidence" that Mr Ortiz was behind the killings. Authorities believe he acted alone.
He referred questions about the investigation to authorities in Webb County and to the Texas Department of Public Safety, whose Texas Rangers are also investigating.