Ortiz was a 10-year veteran of the Border Patrol.
Alaniz told The Associated Press that all the women worked as prostitutes.
Ortiz was arrested after the fifth woman managed to flee.
Further details were sparse.
"The arrest of the border patrol agent who has allegedly committed multiple murders could not have happened without the hard work and expertise of the Texas Rangers, the Webb County Sheriff's Office, the Webb County District Attorney's Office, and Laredo Police Department".
"We have very strong evidence that he is the person who has been killing", Webb County Sheriff Martin Cuellar said at a news conference posted on KGNS's Facebook page.
All of these cases are related to the almost two week murder investigation of two other women who were found killed in a rural part of Webb County.
Investigators found the first three bodies in a remote area in the northwest part of the county, the Laredo Morning Times reported. They also said Ortiz is believed to have been working alone.
Alaniz said investigators are still trying to determine a motive for the killings, though he described Ortiz as a serial killer.
The second victim, 42-year-old Claudine Anne Luera, was located alive along Texas Highway 255 near mile marker 436. The other victims' identities have not yet been released.
"We want to reassure the citizens of Laredo that the community and your families are safe", the Laredo Police Department said in a statement on Saturday afternoon, according to the Houston Chronicle.
In a statement, Andrew Meehan, assistant commissioner for public affairs for U.S. Customs and Border Protection, said his agency is fully cooperating with all investigators.