The suspect accused of killing Harris County Cpl. Charles Galloway earlier this week has been on the run since 1996 and is wanted for another murder in El Salvador, Harris County District Attorney Kim Ogg said Thursday. 

Jose Oscar Rosales, 50, was arrested Wednesday in the Mexican border city of Ciudad de Acuña. Mexican law enforcement took him into custody before turning him over to U.S. authorities.

Oscar Rosales, 51, who police accuse of fatally shooting Harris County Corporal Charles Galloway early Sunday, is likely an alias, authorities said during a Monday news briefing. 

Oscar Rosales, 51, who police accuse of fatally shooting Harris County Corporal Charles Galloway early Sunday, is likely an alias, authorities said during a Monday news briefing.  (Harris County DA/Houston OEM)

Speaking to reporters, Ogg described Rosales as a "professional criminal" who has been a fugitive for 25 years after a warrant was issued on an aggravated assault with a knife charge in Harris County. She said he is also wanted for murder in El Salvador – one of several countries where he has lived.  

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Ogg also said Rosales has "potential gang or cartel affiliation," but did not elaborate. 

"The crime of capital murder can only end two ways: in the death penalty, or in life without parole. This case has all the earmarkings and is a death penalty case," Ogg said, clarifying that her office would weigh all the evidence as it works on the case. 

"The crime of capital murder can only end two ways: in the death penalty, or in life without parole. This case has all the earmarkings and is a death penalty case."

— Kim Ogg, Harris County district attorney
Kim Ogg, Harris County district attorney

Kim Ogg, Harris County district attorney (Twitter)

Rosales is accused of fatally shooting a Galloway, a 47-year-old Houston-area corporal with the Harris County Constable's Office, during a traffic stop this past weekend and was being held without bond Thursday after being returned to the U.S. following his arrest in Mexico.

Authorities were also trying to determine Rosales' immigration status and if he was a citizen of El Salvador, Guatemala or Honduras, Ogg said. 

Jose Oscar Rosales was apprehended in Mexico on Wednesday and transported back to the U.S. for the capital murder of Harris County, Texas Corporal Charles Galloway. 

Jose Oscar Rosales was apprehended in Mexico on Wednesday and transported back to the U.S. for the capital murder of Harris County, Texas Corporal Charles Galloway.  (FOX 29 San Antonio)

An ICE spokesperson previously confirmed to Fox News that Rosales "previously illegally entered the U.S. on an unknown date and at unknown location without inspection or parole by U.S. immigration officials and later fled to Mexico after allegedly murdering a Harris County (Texas) Constable's Office deputy." 

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Authorities were still trying to determine a motive for the shooting of Galloway, Houston police Chief Troy Finner said Thursday. 

"No one can speak to sheer, just evilness -- evilness – and it's hard. I'm not even concerned in asking him that right now. He did it and you know what? He's going to be held accountable. ... How can a human being do that to another human being, especially somebody who's serving? It's just hard to accept. But right now justice is going to be served," Finner said. 

"How can a human being do that to another human being, especially somebody who's serving? It's just hard to accept."

— Chief Troy Finner, Houston police
Jose Oscar Rosales was apprehended in Mexico Wednesday and transported back to the U.S. for the capital murder of Harris County, Texas Corporal Charles Galloway.

Jose Oscar Rosales was apprehended in Mexico Wednesday and transported back to the U.S. for the capital murder of Harris County, Texas Corporal Charles Galloway. (Fox 29/KABB)

Rosales spoke briefly during his appearance in probable-cause court Wednesday evening, commenting on the various officers that surrounded him.

"Right here all the officers and the security guy, that's fine. They want to try (to) kill me right here, they can do it, whatever. I don't care. Everybody right here in this room is waiting for his chance to hurt me," Rosales said.

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Rosales will appear before Harris County’s 482nd criminal court at 9 a.m. Friday.  

The Associated Press contributed to this report.