Pedro Alberto Monterosso aka Navas/Wilson Rigoberto Mena

Immigration officials have placed a detainer on the man suspected of beating his girlfriend to death early Sunday inside their Metairie apartment, then fleeing to Texas with three of his children.

The action means that Immigration and Customs Enforcement will take custody of Pedro Alberto Monterroso-Navas, who allegedly is in the country illegally, whenever he might be released from jail, then likely begin the deportation process.

According to ICE, Monterroso, his five children and his girlfriend, 24-year-old Heidi Monroy, were apprehended in recent weeks when they were found entering the country near the Mexican border.

Monterroso and two children were taken into custody by U.S. Border Patrol agents June 26 in the Rio Grande Valley, said Bryan Cox, an ICE spokesman.

Monroy and three children had been apprehended by Border Patrol agents in the same area May 11.

Everyone was released from custody and issued notices to appear in immigration court after records checks found no criminal history or gang affiliations, Cox said.

Monterroso, a Honduran who also goes by the name Wilson Rigoberto Mina, remained jailed Thursday at the Harris County, Texas, jail, where he was booked Monday on a second-degree murder warrant from Jefferson Parish.

Authorities found him and two of his children in a trailer park near Katy, Texas, hours after the Jefferson Parish Sheriff’s Office issued an Amber Alert and identified him as the suspect in Monroy’s death.

A Jefferson Parish Sheriff’s Office spokesman said officials are in the process of extraditing Monterroso.

Cox said Monterroso will go through the criminal justice system like any other suspect and would serve whatever sentence is handed down if he is convicted. A murder conviction would only increase federal authorities’ desire to deport Monterroso, he said.

“Anyone convicted of murder is in the highest priority for removal,” Cox said.

Monroy was killed early Sunday morning in the bathroom of the apartment in the 4000 block of Durand Street that she shared with Monterroso and five children, apparently three she had with him and two he had with other women.

Neighbors said the family had lived there only a few weeks.

The Sheriff’s Office said Monroy died of blunt-force trauma to her head. Officials have not identified a motive for her death.

Editor’s note: An earlier version of this story said that Jefferson Parish officials declined to comment on if or when they will seek to extradite Monterroso. A Sheriff’s Office spokesman on Friday said that authorities are working to bring him back to Jefferson Parish.

Follow Danny Monteverde on Twitter, @DCMonteverde.